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A Family of Calabi–Yau Varieties and Potential Automorphy II
Open accessAbstract
We prove new potential modularity theorems for n-dimensional essentially self-dual l -adic representations of the absolute Galois group of a totally real field. Most notably, in the ordinary case we prove quite a general result. Our results suffice to show that all the symmetric powers of any non-CM, holomorphic, cuspidal, elliptic modular newform of weight greater than one are potentially cuspidal automorphic. This in turns proves the Sato–Tate conjecture for such forms. (In passing we also note that the Sato–Tate conjecture can now be proved for any elliptic curve over a totally real field.)
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Citations
Cites
Modular Elliptic Curves and Fermat's Last Theorem
Wiles, A. (1995) · The Annals of Mathematics · doi:10.2307/2118559 · Cited by 2,060
Cited by
Automorphy for some l -adic lifts of automorphic mod l Galois representations. II
Taylor, R. (2008) · Publications Mathématiques de l'IHÉS · doi:10.1007/s10240-008-0015-2 · Cited by 316
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Metadata
- Authors
- Barnet-Lamb, T., Geraghty, D., Harris, M., & Taylor, R.
- Venue
- Publications of the Research Institute for Mathematical Sciences
- Published
- 2011-03-24
- Volume
- 47
- Issue
- 1
- Pages
- 29-98
- ISSN
- 0034-5318 (ISSN-L)
- 1663-4926
- OpenAlex
- W2040403535
- Cited by
- 389
- References
- 1
- FWCI
- 34.21
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Barnet-Lamb, T., Geraghty, D., Harris, M., & Taylor, R. (2011). A Family of Calabi–Yau Varieties and Potential Automorphy II. Publications of the Research Institute for Mathematical Sciences. https://doi.org/10.2977/prims/31
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