The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index; 1 of the 27 sources its claims cite were checked for support.
Géométrie algébrique et géométrie analytique
Open accessAbstract
Toute variété algébrique X sur le corps des nombres complexes peut être munie, de façon canonique, d’une structure d’espace analytique ; tout faisceau algébrique cohérent sur X détermine un faisceau analytique cohérent. Lorsque X est une variété projective, nous montrons que, réciproquement, tout faisceau analytique cohérent sur X peut être obtenu ainsi, et de façon unique ; de plus, cette correspondance préserve les groupes de cohomologie. Ces résultats contiennent comme cas particuliers des théorèmes classiques de Chow et Lefschetz, et permettent d’aborder la comparaison entre espaces fibrés algébriques et espaces fibrés analytiques de base une variété algébrique projective.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
Serre proves that for a projective complex algebraic variety, coherent algebraic sheaves and coherent analytic sheaves correspond bijectively and have isomorphic cohomology. This GAGA equivalence yields algebraic-versus-analytic comparison results, including Chow’s theorem and algebraicity criteria for certain principal bundles.
Key findings
- For projective \(X\) over \(\mathbb C\) and any coherent algebraic sheaf \(\mathcal F\), the natural map \(H^q(X,\mathcal F)\to H^q(X^{\mathrm{an}},\mathcal F^{\mathrm{an}})\) is bijective for every \(q\ge 0\) (Theorem 1). Theorems 2 and 3 add that analytic morphisms between associated sheaves come from algebraic morphisms, and every coherent analytic sheaf comes from a coherent algebraic sheaf, uniquely up to isomorphism.
- Applications include invariance of Betti numbers of nonsingular varieties under automorphisms of \(\mathbb C\) (Proposition 12), algebraicity of compact analytic subsets of algebraic varieties (Proposition 14), regularity of holomorphic maps from compact algebraic varieties to algebraic varieties (Proposition 15), and uniqueness of an algebraic structure on a compact analytic space (corollary).
- For principal bundles, the algebraic-to-analytic comparison map is injective for compact \(X\) (Proposition 16) and bijective for the additive group \(\mathbb C\) (Proposition 17), for \(\mathrm{GL}_n(\mathbb C)\) (Proposition 18), and for groups satisfying a rational-section condition (R), including solvable groups, \(\mathrm{SL}_n(\mathbb C)\), and \(\mathrm{Sp}_{2m}(\mathbb C)\) (Proposition 20 examples).
- Locally, the algebraic local ring and the ring of holomorphic germs at a point have the same completion and form a flat couple; consequently they have the same dimension (Proposition 3, Corollaries 1–2).
Methods
- The paper is a mathematical proof study: it defines analytic spaces following H. Cartan, constructs the analytic space \(X^{\mathrm{an}}\) associated to a complex algebraic variety, and compares local rings and sheaves on \(X\) and \(X^{\mathrm{an}}\).
- The main arguments use coherent algebraic sheaf theory, Cartan’s Theorems A and B, exact sequences of sheaves, the five lemma, induction on cohomological degree and dimension, and Dolbeault theory for Betti-number applications.
- There is no empirical sample or dataset; the analysis is local and global sheaf cohomology together with commutative algebra of local rings, completions, and flat couples.
Limitations
- The author states that the fiber-space applications are incomplete: among semisimple groups, only the unimodular linear group and the symplectic group are treated, and applications to automorphic functions are left aside.
- The author notes uncertainty about whether \(X\) and its transform \(X^\sigma\) are always homeomorphic; a genus-1 curve example shows they are not always analytically isomorphic. The rational-section condition (R) fails for \(\mathrm{O}_n(\mathbb C)\) when \(n\ge 3\), and bijectivity in that case is unknown.
- Evident from the text: the main equivalence theorems require projectivity and fail even for affine varieties; several applications also assume nonsingularity or compactness.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
1 of 27 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured
In the paper
“COROLLAIRE 1. -Le couple £ anneaux (Q^ 3€^) est un couple plat”
§ ANNALES DE L'INSTITUT FOURIER > 5. Définition de l'espace analytique associé à une variété algébrique.
What the sources say
- Not matchedcites Annexe, déf.4
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Not matched
In the paper
“LEMME 3. -Soit A un anneau commutatif, dans lequel Vidéal 0 soit intersection Sun nombre fini d^idéaux premiers minimaux distincts p;; soit K^ le corps des fractions de A/p^, et soit S V ensemble des éléments de A qui ^appartiennent à aucun des pc U anneau de fractions As est alors isomorphe au composé direct des K,.”
§ ANNALES DE L'INSTITUT FOURIER > As c As.
What the sources say
- Not matchedcites [15] [15] P. Samuel. Commutative Algebra (Notes by D. Herzig). Cornell Univ., 1953.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“La topologie de X^ est plus fine que la topologie de X”
§ ANNALES DE L'INSTITUT FOURIER > 5. Définition de l'espace analytique associé à une variété algébrique.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“b) 5i Y est un sous-espace analytique fermé de X, le faisceau .^)(Y)est un faisceau analytique cohérent”
§ ANNALES DE L'INSTITUT FOURIER > 3. Faisceaux analytiques.
What the sources say
- Not matchedcites [1] [1] H. Cartan. Idéaux et modules de fonctions analytiques de variables complexes. Bull. Soc. Math. France, 78, 1950, pp. 29-64.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [2] [2] H. Cartan. Séminaire E. N. S., 1951-1952.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“COROLLAIRE 3. -Si X est une variété algébrique irréductible de dimension r, l'espace analytique X^ est de dimension analytique r en chacun de ses points”
§ ANNALES DE L'INSTITUT FOURIER > COROLLAIRE 2. -Les anneaux Oy; et Mp ont même dimension.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“COROLLAIRE 2. -Les anneaux Oy; et Mp ont même dimension.”
§ ANNALES DE L'INSTITUT FOURIER > COROLLAIRE 2. -Les anneaux Oy; et Mp ont même dimension.
What the sources say
- Not matchedcites [16] [16] P. Samuel. Algèbre locale. Mém. Sci. Math., 123, Paris, 1953.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“la correspondance entre ces deux catégories de faisceaux laisse invariants les groupes de cohomologie”
§ ANNALES DE L'INSTITUT FOURIER > INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“II existe sur X une structure d'espace analytique et une seule telle que, pour toute carte ç : V ->-U, Fensemble Z-owert V soit ouvert, et y soit un isomorphisme analytique de V”
§ ANNALES DE L'INSTITUT FOURIER > 5. Définition de l'espace analytique associé à une variété algébrique.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: A polynomial is continuous for the usual topology and holomorphic.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“PROPOSITION 5. -Soient X une variété algébrique^ et U une partie de X. Si U est ï-owerte et ï-dense dans X, alors U est dense dans X.”
§ ANNALES DE L'INSTITUT FOURIER > COROLLAIRE 2. -Les anneaux Oy; et Mp ont même dimension.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“PROPOSITION 6. ^-Pour qu'une variété algébrique X soit complète, il faut et il suffit quelle soit compacte.”
§ ANNALES DE L'INSTITUT FOURIER > PROPOSITION 6. ^-Pour qu'une variété algébrique X soit complète, il faut et il suffit quelle soit compacte.
What the sources say
- Not matchedcites [7] [7] W-L. Chow. On the projective embedding of homogeneous varieties. Lefschetz's volume, Princeton, 1956.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [19] [19] J.-P. Serre. Sur la cohomologie des variétés algébriques. J. de Maths. Pures et Appl., 35, 1956.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: Every projective algebraic variety is compact in the usual topology.
- Not matched
- It may state two separate claims as one. 7
- The quote only partly states this claim. 4
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Pour n = 1, GL^(C) coïncide avec le groupe multiplicatif C*; si l'on suppose que X est une variété normale, le groupe H 1 (X, fî) coïncide avec le groupe des classes de diviseurs localement linéairement équivalents à zéro (cf.[20], § 3) et la proposition 18 signifie que tout espace fibre analytique de base X et de groupe structural C* provient d'un tel diviseur.”
§ ANNALES DE L'INSTITUT FOURIER > 20. Espaces fibres algébriques et espaces fibres analytiques.
What the sources say
- Not matchedcites [20] [20] A. Weil. Fibre-spaces in algebraic geometry (Notes by A. Wallace). Chicago Univ., 1952.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Partly supportedcites [12] [12] K. Kodaira and D. C. Spencer. Divisor class groups on algebraic varieties. Proc. Nat. Acad. Sci. U. S. A., 39, 1953, pp. 872-877. sourceExperimental — accuracy not yet measured
In the opening discussion and Theorem 1 (pages not supplied), the paper identifies divisor classes with complex line bundles and proves that every such bundle comes from a divisor. Its stated setting is a non-singular projective algebraic variety, however; it does not establish the cited identification of H¹(X,O*) with those divisor classes for an arbitrary normal X. The statement about Proposition 18 is the citing author's own interpretation, not a result attributed to this source. (LLM, conf=0.84)
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“X^ est un espace localement compact dénombrable à Vinfini.”
§ ANNALES DE L'INSTITUT FOURIER > 5. Définition de l'espace analytique associé à une variété algébrique.
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“faisceaux algébriques cohérents et faisceaux analytiques cohérents se correspondent biunivoquement”
§ ANNALES DE L'INSTITUT FOURIER > INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Le faisceau 3^ est un faisceau de 3-6-modules, c'est-à-dire un faisceau analytique', l'injection 0'-^ 3^ définit un homomorphisme canonique a : 9' ->-9^.”
§ ANNALES DE L'INSTITUT FOURIER > As c As.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“THÉORÈME 3 . -Pour tout faisceau analytique cohérent jll» sur X 71 , il existe un faisceau algébrique cohérent ^ sur X tel que ^ soit isomorphe à JIL.De plus, cette propriété détermine 9 de façon unique, à un isomorphisme près.”
§ ANNALES DE L'INSTITUT FOURIER > £: E^JL^Ê.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Pour tout a;çX, on a donc 3^ == 3^; les faisceaux 9 et y ne diffèrent que par leur topologie (9' n'est pas autre chose que V image réciproque de 9 par l'application continue X^X).”
§ ANNALES DE L'INSTITUT FOURIER > As c As.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“En vertu du lemme 8, il existe un entier n tel que M)(n) soit isomorphe à un faisceau quotient d'un faisceau 3^, et M) est donc isomorphe à un quotient de Wo (-n^.”
§ ANNALES DE L'INSTITUT FOURIER > 16. Démonstration du théorème 3. Les faisceaux ll(n).
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Les deux faisceaux en question sont nuls en dehors de Y^; il nous suffira donc de montrer que leurs restrictions à Y 71 sont isomorphes.”
§ ANNALES DE L'INSTITUT FOURIER > 10. Prolongement d'un faisceau.
What the sources say
- Not matchedcites [18] [18] J.-P. Serre. Faisceaux algébriques cohérents. Ann. of Maths., 61, 1955, pp. 197-278.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Ces trois théorèmes signifient que la théorie des faisceaux analytiques cohérents sur X^ coïncide essentiellement avec celle des faisceaux algébriques cohérents sur X. Bien entendu, ils tiennent à ce que X est une variété projectile, et sont inexacts même pour une variété affine.”
§ ANNALES DE L'INSTITUT FOURIER > On a alors :
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“c) lorsque G == Sj^(C), n = 2m; dans ce cas, l'espace homogène GL^(C)/G est l'espace des formes alternées non dégénérées”
§ ANNALES DE L'INSTITUT FOURIER > £: E^JL^Ê.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
The paper relies on this without support.
Every projective algebraic variety is compact in the usual topology.
“comme toute variété projective est compacte pour la topologie usuelle”
The paper relies on this without support.
The fraction field of the local ring of an irreducible component of an algebraic variety at a point is the field of rational functions on that component.
“le corps des quotients de A;, soit K(, n'est donc pas autre chose que le corps des fonctions rationnelles sur la variété irréductible X^.”
The paper relies on this without support.
A polynomial is continuous for the usual topology and holomorphic.
“comme un polynôme est continu pour la topologie usuelle (resp.holomorphe)”
Citations
Cites
Some Basic Theorems on Algebraic Groups
Rosenlicht, M. (1956) · American Journal of Mathematics · doi:10.2307/2372523 · Cited by 495
On Compact Complex Analytic Varieties
Chow, W.-L. (1949) · American Journal of Mathematics · doi:10.2307/2372375 · Cited by 132
Divisor class groups on algebraic varieties
Kodaira, K., & Spencer, D. C. (1953) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.39.8.872 · Cited by 39
Zum Eliminationsproblem der Potenzreihenideale
Rückert, W. (1932) · Springer eBooks · doi:10.1007/978-3-662-41142-1_1 · Cited by 23
Fibre-spaces in algebraic geometry
WEIL, A. A. (1979) · Springer eBooks · doi:10.1007/978-1-4757-1705-1_51 · Cited by 9
Flagged first, then by citations
Research works printed but not linked: 7
- [1] H. Cartan. Idéaux et modules de fonctions analytiques de variables complexes. Bull. Soc. Math. France, 78, 1950, pp. 29-64.
- [5] H. Cartan et J.-P. Serre. Un théorème de finitude concernant les variétés analytiques compactes. C. R., 237, 1953, pp. 128-130.
- [8] P. Dolbeault. Sur la cohomologie des variétés analytiques complexes. C. R., 236, 1953, pp. 175-177.
- [9] J. Frenkel. Cohomologie à valeurs dans un faisceau non abélien. C. R., 240, 1955, pp. 2368-2370.
- [11] K. Kodaira. On Kähler varieties of restricted type (an intrinsic characterization of algebraic varieties). Ann. of Maths., 60, 1954, pp. 28-48.
- [17] P. Samuel. Méthodes d'algèbre abstraite en géométrie algébrique. Ergebn. der Math., Springer, 1955.
- [18] J.-P. Serre. Faisceaux algébriques cohérents. Ann. of Maths., 61, 1955, pp. 197-278.
Cited by
Sorted by citations
Items 601–651 of 651
Commentaries on Hellmuth Kneser’s Papers in Complex Function Theory
(2011) · De Gruyter eBooks · doi:10.1515/9783110894516.857
The ring of germs of smooth functions
Montaldi, J. A. (2021) · Cambridge University Press eBooks · doi:10.1017/9781316585085.004
(1982) · Pure and applied mathematics · doi:10.1016/s0079-8169(08)61274-x
Families of maps and bifurcations
Montaldi, J. (2021) · Cambridge University Press eBooks · doi:10.1017/9781316585085.011
Montaldi, J. A. (2021) · Cambridge University Press eBooks · doi:10.1017/9781316585085.012
Constrained bifurcation problem
Montaldi, J. A. (2021) · Cambridge University Press eBooks · doi:10.1017/9781316585085.024
Differential equations and Lie group representations
Lai, K. F. (2022) · Frontiers of Mathematics · doi:10.1007/s11464-022-1008-z
Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties
Yao, Q. (2024) · Canadian Journal of Mathematics · doi:10.4153/s0008414x24000464
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.001
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.004
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.005
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.008
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.009
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.002
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.007
Ogus, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316941614.003
A regular interpolation problem and its applications
Das, N. (2023) · Communications in Algebra · doi:10.1080/00927872.2023.2177662
“For more details about the analytic properties of complex algebraic varieties, morphisms, and their connections with the algebraic properties, we refer the reader to [10].”
BackgroundConnections and genuinely ramified maps of curves
Biswas, I., Machu, F.-X., & Parameswaran, A. J. (2023) · Forum Mathematicum · doi:10.1515/forum-2022-0343
GENERALISED AUTOMORPHIC SHEAVES AND THE PROPORTIONALITY PRINCIPLE OF HIRZEBRUCH-MUMFORD
Hörmann, F. (2023) · Journal of the Institute of Mathematics of Jussieu · doi:10.1017/s1474748023000300
Asymptotic behavior of the Zhang–Kawazumi's φ-invariants
Song, Y. (2023) · Advances in Mathematics · doi:10.1016/j.aim.2023.109349
Universally irreducible subvarieties of Siegel moduli spaces
Mondello, G., & Manni, R. S. (2023) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crelle-2023-0078
On the component group of the algebraic monodromy group of a K3 surface
Elsenhans, A.-S., & Jahnel, J. (2024) · Journal of Algebra · doi:10.1016/j.jalgebra.2024.02.005
Pushforward of structure sheaf and virtual global generation
Biswas, I., Kumar, M., & Parameswaran, A. J. (2024) · Proceedings of the Edinburgh Mathematical Society · doi:10.1017/s001309152400021x
Locally semialgebraic superspaces and Nash supermanifolds
Can, M. B. (2024) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/804/16111
Vanishing of local cohomology with applications to Hodge theory
Hiatt, S. (2024) · Journal of Algebra · doi:10.1016/j.jalgebra.2024.07.036 · Cited by 1
Szczeciniarz, J.-J. (2024) · Chapman mathematical notes · doi:10.1007/978-3-031-68934-5_7
Dovbush, P. V., & Krantz, S. G. (2025) · Springer eBooks · doi:10.1007/978-3-031-77204-7_14
Group Actions and Riemann Surfaces
Paulhus, J. (2024) · Association for Women in Mathematics series · doi:10.1007/978-3-031-81217-0_2
Uniform bundles and the GAGA shift from Van de Ven to Ballico
Hirschowitz, A. (2025) · Bollettino Della Unione Matematica Italiana · doi:10.1007/s40574-025-00461-y
“GAGA is the standard acronym for a famous contribution of Jean-Pierre Serre entitled Géométrie algébrique et géométrie analytique [47] where the correspondence between complex algebraic geometry and complex analytic geometry is masterfully clarified.”
Chow Varieties and Cycle Spaces
Barlet, D., & Magnússon, J. (2025) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-031-84845-2_5
Symplectic leaves in projective spaces of bundle extensions
Chirvasitu, A. (2025) · Advances in Mathematics · doi:10.1016/j.aim.2025.110515 · Cited by 1
1The early years: flatness, projectivity, and R -sequences
Brennan, J. P., & Nielander, T. (2025) · De Gruyter eBooks · doi:10.1515/9783110999365-001
Tensor Products of Quiver Bundles
Numpaque-Roa, J. S. (2025) · The Quarterly Journal of Mathematics · doi:10.1093/qmath/haaf038
GAGA type results for singularity categories
Wu, Y., Xu, J., & Zhou, G. (2025) · Journal of Pure and Applied Algebra · doi:10.1016/j.jpaa.2025.108146
Local monomialization of generalized real analytic functions
Villaverde, R. M. (2011) · theses.fr (ABES) · doi:10.70675/2fcb2fa1ze3a8z4e9ezb1b4zb9011ebc4a21
Application de Riemann-Hilbert-Birkhoff
Paolantoni, T. (2017) · theses.fr (ABES) · doi:10.70675/4cb78d53z8eeez4799zb115zb5d169a79f76
Height of cycles in toric varieties
Gualdi, R. (2018) · theses.fr (ABES) · doi:10.70675/fce8dc3fz2833z4c0azbd36z31b2bd26d190
K-stability and Kähler manifolds with transcendental cohomology class
Dyrefelt, Z. S. (2017) · theses.fr (ABES) · doi:10.70675/04711a02zda2ez4994za162z4fc4d6b4d812
l-adic,p-adic and geometric invariants in families of varieties.
Ambrosi, E. (2019) · theses.fr (ABES) · doi:10.70675/4954dc59z975az4205za352zcd7df06efeb0 · Cited by 1
Analytic moduli spaces of non quasi-homogeneous functions
Loubani, J. (2018) · theses.fr (ABES) · doi:10.70675/e50bb2f4zd87az4400z986bz1a456e5d56b2
Cohomology groups of holomorphic bundles and Chern classes
Wu, X. (2020) · theses.fr (ABES) · doi:10.70675/d95c721ez84b3z4d2czaa87z3afd0bda384f
Géométrie et arithmétique des composantes des espaces de Hurwitz
Seguin, B. (2023) · theses.fr (ABES) · doi:10.70675/78f0769ez5645z4955z8c6cze263d6020355
Towards a categorical resolution of some singular moduli spaces on a K3 surface
Martinelli, L. (2023) · theses.fr (ABES) · doi:10.70675/213b143bz07e9z4dc9zacd6z77cf4d535c80
Integral points, monodromy, generic vanishing and Fourier-Mukai transform
Liu, H. (2024) · theses.fr (ABES) · doi:10.70675/bbd90528z684ez45c3za9c3z0ac0a0670b60
Baily–Borel Compactifications for Period Images
Tsimerman, J. (2026) · doi:10.1137/25m1807368
Finiteness of Pythagoras numbers of finitely generated real algebras
Ouyang, Y., Song, Q., & Zhang, C. (2026) · Communications in Algebra · doi:10.1080/00927872.2026.2705360
Non-abelian Hodge theory and moduli spaces of Higgs bundles
Gallego, G. (2026) · Revista de Matemática Teoría y Aplicaciones · doi:10.15517/dg20cm45
Jean-Pierre Serre: Mon premier demi-siècle au Collège de France
Kirsch, M. (2009) · The Abel prize · doi:10.1007/978-3-642-01373-7_3
Fibrati Vettoriali sulle Curve
Bottacin, F. (1996)
Metadata
- Authors
- Serre, J.-P.
- Corresponding author
- Serre, Jean-Pierre
- ORCID
- Serre, Jean-Pierre
- Venue
- Annales de l'Institut Fourier
- Publisher
- MathDoc/Centre Mersenne
- Published
- 1956
- Volume
- 6
- Pages
- 1-42
- ISSN
- 0373-0956 (ISSN-L)
- 1777-5310
- OpenAlex
- W2092940386
- Cited by
- 645
- References
- 4
- Citations by year
- 2026: 6 · 2025: 12 · 2024: 15 · 2023: 22 · 2022: 19 · 2021: 62 · 2020: 28 · 2019: 26 · 2018: 27 · 2017: 20 · 2016: 16 · 2015: 9 · 2014: 15 · 2013: 10 · 2012: 12
- FWCI
- 6.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Annales de l’institut Fourier (publishedVersion)
- Annals of the Fourier Institute (Institut Fourier) (submittedVersion)
- French digital mathematics library (Numdam) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Algebra and Geometry
- Keywords
- analytic spaces, coherent sheaves, projective varieties, cohomology groups, Lefschetz theorem
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-09-28, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-09-28 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
