The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
Open accessAbstract
We complete the proof that every elliptic curve over the rational numbers is modular.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Grothendieck, A. (1964) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684747 · Cited by 2,824
Modular Elliptic Curves and Fermat's Last Theorem
Wiles, A. (1995) · The Annals of Mathematics · doi:10.2307/2118559 · Cited by 2,060
Introduction to the Arithmetic Theory of Automorphic Functions
Tretkoff, M., & Shimura, G. (1972) · Mathematics of Computation · doi:10.2307/2005900 · Cited by 2,010
Éléments de géométrie algébrique : I. Le langage des schémas
Grothendieck, A. (1960) · Publications mathématiques de l IHÉS · doi:10.1007/bf02684778 · Cited by 1,722
Ring-Theoretic Properties of Certain Hecke Algebras
Taylor, R., & Wiles, A. (1995) · The Annals of Mathematics · doi:10.2307/2118560 · Cited by 1,016
Self-citationEndlichkeitss�tze f�r abelsche Variet�ten �ber Zahlk�rpern
Faltings, G. (1983) · Inventiones mathematicae · doi:10.1007/bf01388432 · Cited by 959
Sur les représentations modulaires de degré 2 de Gal(Q¯/Q)
Serre, J.-P. (1987) · Duke Mathematical Journal · doi:10.1215/s0012-7094-87-05413-5 · Cited by 471
Formes modulaires de poids $1$
Deligne, P., & Serre, J.-P. (1974) · Annales scientifiques de l'École normale supérieure · doi:10.24033/asens.1277 · Cited by 462
Langlands, R. P. (1980) · Princeton University Press , University of Tokyo Press eBooks · Cited by 279
�ber die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen
Weil, A. (1967) · Mathematische Annalen · doi:10.1007/bf01361551 · Cited by 242
Metadata
- Authors
- Breuil, C., Conrad, B., Diamond, F., & Taylor, R.
- Venue
- Journal of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 2001-05-15
- Volume
- 14
- Issue
- 4
- Pages
- 843-939
- ISSN
- 0894-0347 (ISSN-L)
- 1088-6834
- OpenAlex
- W1868013030
- Cited by
- 746
- References
- 19
- FWCI
- 40.10
- Type
- journal article
- Language
- en
- Open access
- bronze
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.
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises. https://app.cochat.ai/papers/10.1090/s0894-0347-01-00370-8
- The paper
- Breuil, C., Conrad, B., Diamond, F., & Taylor, R. (2001). On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises. Journal of the American Mathematical Society. https://doi.org/10.1090/s0894-0347-01-00370-8
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.