Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
Publications Mathématiques de l'IHÉS, Tome 108 (2008), pp. 183-239.

We extend the results of [CHT] by removing the ‘minimal ramification' condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara's lemma.

@article{PMIHES_2008__108__183_0,
     author = {Taylor, Richard},
     title = {Automorphy for some $l$-adic lifts of automorphic mod $l$ {Galois} representations. {II}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {183--239},
     publisher = {Springer-Verlag},
     volume = {108},
     year = {2008},
     doi = {10.1007/s10240-008-0015-2},
     mrnumber = {2470688},
     zbl = {1169.11021},
     language = {en},
     url = {https://www.numdam.org/articles/10.1007/s10240-008-0015-2/}
}
TY  - JOUR
AU  - Taylor, Richard
TI  - Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II
JO  - Publications Mathématiques de l'IHÉS
PY  - 2008
SP  - 183
EP  - 239
VL  - 108
PB  - Springer-Verlag
UR  - https://www.numdam.org/articles/10.1007/s10240-008-0015-2/
DO  - 10.1007/s10240-008-0015-2
LA  - en
ID  - PMIHES_2008__108__183_0
ER  - 
%0 Journal Article
%A Taylor, Richard
%T Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II
%J Publications Mathématiques de l'IHÉS
%D 2008
%P 183-239
%V 108
%I Springer-Verlag
%U https://www.numdam.org/articles/10.1007/s10240-008-0015-2/
%R 10.1007/s10240-008-0015-2
%G en
%F PMIHES_2008__108__183_0
Taylor, Richard. Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II. Publications Mathématiques de l'IHÉS, Tome 108 (2008), pp. 183-239. doi : 10.1007/s10240-008-0015-2. https://www.numdam.org/articles/10.1007/s10240-008-0015-2/

1. J. Arthur and L. Clozel, Simple Algebras, Base Change and the Advanced Theory of the Trace Formula, Ann. Math. Stud., vol. 120, Princeton University Press, 1989. | MR | Zbl

2. C. Breuil, A. Mezard, Multiplicités modulaires et représentations de GL2(Z p ) et de Gal(𝐐¯p/𝐐p) en ℓ=p , Duke Math. J. 115 (2002), p. 205-310 | MR | Zbl

3. L. Clozel, M. Harris, and R. Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations, this volume. | Numdam | MR | Zbl

4. D. Eisenbud, Commutative Algebra with a View Towards Algebraic Geometry, Springer, 1994. | MR | Zbl

5. A. Grothendieck, Eléments de géométrie algébrique. IV. Etude locale des schémas et des morphismes de schémas. III., Publ. Math., Inst. Hautes Étud. Sci., 28 (1966). | Numdam | Zbl

6. M. Harris, N. Shepherd-Barron, and R. Taylor, Ihara's lemma and potential automorphy, Ann. Math., to appear.

7. M. Harris and R. Taylor, The Geometry and Cohomology of some Simple Shimura Varieties, Ann. Math. Stud., vol. 151, Princeton University Press, 2001. | MR | Zbl

8. M. Kisin, Moduli of finite flat groups schemes and modularity, Ann. Math., to appear. | MR | Zbl

9. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986. | MR | Zbl

10. C. Skinner, A. Wiles, Base change and a problem of Serre, Duke Math. J. 107 (2001), p. 15-25 | MR | Zbl

11. R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. Math. 141 (1995), p. 553-572 | MR | Zbl

12. R. Taylor, T. Yoshida, Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc. 20 (2007), p. 467-493 | MR | Zbl

13. A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. Math. 141 (1995), p. 443-551 | MR | Zbl

  • Boxer, George; Calegari, Frank; Gee, Toby; Newton, James; Thorne, Jack A. The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms, Forum of Mathematics, Pi, Volume 13 (2025) | DOI:10.1017/fmp.2024.29
  • Banaszak, Grzegorz; Farfán, Victoria Cantoral A remark on the component group of the Sato–Tate group, Research in Number Theory, Volume 11 (2025) no. 1 | DOI:10.1007/s40993-024-00555-0
  • Lee, Kyu-Hwan; Oh, Se-Jin Auto-Correlation Functions for Unitary Groups, Algebras and Representation Theory, Volume 27 (2024) no. 1, p. 583 | DOI:10.1007/s10468-023-10225-x
  • Shotton, Jack Irreducible Components of the Moduli Space of Langlands Parameters, International Mathematics Research Notices, Volume 2024 (2024) no. 11, p. 9020 | DOI:10.1093/imrn/rnad274
  • Blaser, Avalon; Bradley, Molly; Vargas, Daniel A.N.; Xing, Kathy Sato–Tate type distributions for matrix points on elliptic curves and some K3 surfaces, Journal of Number Theory, Volume 260 (2024), p. 173 | DOI:10.1016/j.jnt.2024.01.010
  • Glazer, Itay; Hendel, Yotam On Singularity Properties of Word Maps and Applications to Probabilistic Waring Type Problems, Memoirs of the American Mathematical Society, Volume 299 (2024) no. 1497 | DOI:10.1090/memo/1497
  • Ray, Anwesh; Weston, Tom Arithmetic statistics for Galois deformation rings, The Ramanujan Journal, Volume 64 (2024) no. 3, p. 685 | DOI:10.1007/s11139-024-00839-0
  • Amri, Mohammed Amin Chebotarev–Sato–Tate distribution for abelian surfaces potentially of GL2-type, European Journal of Mathematics, Volume 9 (2023) no. 4 | DOI:10.1007/s40879-023-00682-5
  • Eyidoğan, Sadık; Göral, Haydar; Kutlu, Mustafa Kutay Arithmetic progressions in certain subsets of finite fields, Finite Fields and Their Applications, Volume 91 (2023), p. 102264 | DOI:10.1016/j.ffa.2023.102264
  • Saad, Hasan Explicit Sato–Tate type distribution for a family of K ⁢ 3 K3 surfaces, Forum Mathematicum, Volume 35 (2023) no. 4, p. 1105 | DOI:10.1515/forum-2022-0272
  • Blomer, Valentin; Michel, Philippe The unipotent mixing conjecture, Journal d'Analyse Mathématique, Volume 151 (2023) no. 1, p. 25 | DOI:10.1007/s11854-023-0326-8
  • Goodson, Heidi Sato–Tate Distributions of Catalan Curves, Journal de théorie des nombres de Bordeaux, Volume 35 (2023) no. 1, p. 87 | DOI:10.5802/jtnb.1238
  • Kim, Seoyoung The Sato-Tate conjecture and Nagao's conjecture, Journal of Number Theory, Volume 242 (2023), p. 245 | DOI:10.1016/j.jnt.2022.04.008
  • Xi, Ping Bilinear forms with trace functions over arbitrary sets and applications to Sato-Tate, Science China Mathematics, Volume 66 (2023) no. 12, p. 2819 | DOI:10.1007/s11425-022-2184-9
  • Acharya, R.; Drappeau, S.; Ganguly, S.; Ramaré, O. A modular analogue of a problem of Vinogradov, The Ramanujan Journal, Volume 62 (2023) no. 2, p. 365 | DOI:10.1007/s11139-022-00688-9
  • Lee, Kyu-Hwan; Oh, Se-jin Auto-correlation functions of Sato–Tate distributions and identities of symplectic characters, Advances in Mathematics, Volume 401 (2022), p. 108309 | DOI:10.1016/j.aim.2022.108309
  • Kozioł, Karol; Morra, Stefano Serre weight conjectures for p-adic unitary groups of rank 2, Algebra Number Theory, Volume 16 (2022) no. 9, p. 2005 | DOI:10.2140/ant.2022.16.2005
  • Gee, Toby Modularity lifting theorems, Essential Number Theory, Volume 1 (2022) no. 1, p. 73 | DOI:10.2140/ent.2022.1.73
  • Naik, Sunil L. On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms, Forum Mathematicum, Volume 0 (2022) no. 0 | DOI:10.1515/forum-2022-0055
  • Emory, Melissa; Goodson, Heidi Sato-Tate distributions of y2 = x − 1 and y2 = x2 − 1, Journal of Algebra, Volume 597 (2022), p. 241 | DOI:10.1016/j.jalgebra.2022.01.002
  • Wong, Peng-Jie Selberg's orthogonality conjecture and symmetric power L-functions, Journal of Number Theory, Volume 238 (2022), p. 967 | DOI:10.1016/j.jnt.2021.11.001
  • He, Yang-Hui; Lee, Kyu-Hwan; Oliver, Thomas Machine-learning the Sato–Tate conjecture, Journal of Symbolic Computation, Volume 111 (2022), p. 61 | DOI:10.1016/j.jsc.2021.11.002
  • Newton, James Modularity of Galois Representations and Langlands Functoriality, Journal of the Indian Institute of Science, Volume 102 (2022) no. 3, p. 861 | DOI:10.1007/s41745-022-00305-0
  • Gee, Toby; Newton, James PATCHING AND THE COMPLETED HOMOLOGY OF LOCALLY SYMMETRIC SPACES, Journal of the Institute of Mathematics of Jussieu, Volume 21 (2022) no. 2, p. 395 | DOI:10.1017/s1474748020000158
  • Calegari, Frank; Emerton, Matthew; Gee, Toby GLOBALLY REALIZABLE COMPONENTS OF LOCAL DEFORMATION RINGS, Journal of the Institute of Mathematics of Jussieu, Volume 21 (2022) no. 2, p. 533 | DOI:10.1017/s1474748020000195
  • Anastassiades, Christos; Thorne, Jack A. RAISING THE LEVEL OF AUTOMORPHIC REPRESENTATIONS OF OF UNITARY TYPE, Journal of the Institute of Mathematics of Jussieu, Volume 21 (2022) no. 4, p. 1421 | DOI:10.1017/s1474748020000602
  • Agwu, Anthony; Harris, Phillip; James, Kevin; Kannan, Siddarth; Li, Huixi Frobenius distributions of elliptic curves in short intervals on average, The Ramanujan Journal, Volume 58 (2022) no. 1, p. 75 | DOI:10.1007/s11139-021-00449-0
  • Moss, Gilbert The universal unramified module for GL(n) and the Ihara conjecture, Algebra Number Theory, Volume 15 (2021) no. 5, p. 1181 | DOI:10.2140/ant.2021.15.1181
  • Böckle, Gebhard; Khare, Chandrashekhar B.; Manning, Jeffrey Wiles defect for Hecke algebras that are not complete intersections, Compositio Mathematica, Volume 157 (2021) no. 9, p. 2046 | DOI:10.1112/s0010437x21007454
  • Duan, Lian; Wang, Biao; Yi, Shaoyun Analogues of Alladi's formula over global function fields, Finite Fields and Their Applications, Volume 74 (2021), p. 101874 | DOI:10.1016/j.ffa.2021.101874
  • Pan, Lue The Fontaine-Mazur conjecture in the residually reducible case, Journal of the American Mathematical Society (2021) | DOI:10.1090/jams/991
  • Manning, Jeffrey; Shotton, Jack Ihara’s Lemma for Shimura curves over totally real fields via patching, Mathematische Annalen, Volume 379 (2021) no. 1-2, p. 187 | DOI:10.1007/s00208-020-02048-8
  • Tung, Shen-Ning On the modularity of 2-adic potentially semi-stable deformation rings, Mathematische Zeitschrift, Volume 298 (2021) no. 1-2, p. 107 | DOI:10.1007/s00209-020-02588-4
  • Newton, James; Thorne, Jack A. Symmetric power functoriality for holomorphic modular forms, Publications mathématiques de l'IHÉS, Volume 134 (2021) no. 1, p. 1 | DOI:10.1007/s10240-021-00127-3
  • Boxer, George; Calegari, Frank; Gee, Toby; Pilloni, Vincent Abelian surfaces over totally real fields are potentially modular, Publications mathématiques de l'IHÉS, Volume 134 (2021) no. 1, p. 153 | DOI:10.1007/s10240-021-00128-2
  • Guiraud, David-Alexandre Unobstructedness of Galois deformation rings associated to regular algebraic conjugate self-dual cuspidal automorphic representations, Algebra Number Theory, Volume 14 (2020) no. 6, p. 1331 | DOI:10.2140/ant.2020.14.1331
  • Allen, Patrick B.; Newton, James; Thorne, Jack A. Automorphy lifting for residually reducible -adic Galois representations, II, Compositio Mathematica, Volume 156 (2020) no. 11, p. 2399 | DOI:10.1112/s0010437x20007484
  • LE, DANIEL; LE HUNG, BAO V.; LEVIN, BRANDON; MORRA, STEFANO SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE, Forum of Mathematics, Pi, Volume 8 (2020) | DOI:10.1017/fmp.2020.1
  • Baier, Stephan; Prabhu, Neha; Sinha, Kaneenika Central limit theorems for elliptic curves and modular forms with smooth weight functions, Journal of Mathematical Analysis and Applications, Volume 485 (2020) no. 1, p. 123709 | DOI:10.1016/j.jmaa.2019.123709
  • Lü, Guangshi Aperiodicity of signs of Hecke eigenvalues, Monatshefte für Mathematik, Volume 191 (2020) no. 1, p. 187 | DOI:10.1007/s00605-019-01347-w
  • Booher, Jeremy Minimally ramified deformations when, Compositio Mathematica, Volume 155 (2019) no. 1, p. 1 | DOI:10.1112/s0010437x18007546
  • Dal Negro, Luca; Chen, Yuyao; Sgrignuoli, Fabrizio Aperiodic Photonics of Elliptic Curves, Crystals, Volume 9 (2019) no. 9, p. 482 | DOI:10.3390/cryst9090482
  • Shparlinski, Igor E. The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields, International Journal of Number Theory, Volume 15 (2019) no. 03, p. 469 | DOI:10.1142/s1793042119500246
  • Sasaki, Shu Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms, Inventiones mathematicae, Volume 215 (2019) no. 1, p. 171 | DOI:10.1007/s00222-018-0825-x
  • Baier, Stephan; Prabhu, Neha Moments of the error term in the Sato–Tate law for elliptic curves, Journal of Number Theory, Volume 194 (2019), p. 44 | DOI:10.1016/j.jnt.2018.07.005
  • Wong, Peng-Jie On the Chebotarev–Sato–Tate phenomenon, Journal of Number Theory, Volume 196 (2019), p. 272 | DOI:10.1016/j.jnt.2018.09.010
  • Gallagher, Katherine; Li, Lucia; Sweeting, Naomi; Vassilev, Katja; Woo, Katharine Generating functions for power moments of elliptic curves over Fp, Journal of Number Theory, Volume 201 (2019), p. 53 | DOI:10.1016/j.jnt.2019.01.019
  • Geraghty, David Modularity lifting theorems for ordinary Galois representations, Mathematische Annalen, Volume 373 (2019) no. 3-4, p. 1341 | DOI:10.1007/s00208-018-1742-4
  • Goresky, Mark; Tai, Yung sheng Ordinary points mod p of GLn(ℝ)-locally symmetric spaces, Pacific Journal of Mathematics, Volume 303 (2019) no. 1, p. 165 | DOI:10.2140/pjm.2019.303.165
  • David, C.; Gafni, A.; Malik, A.; Prabhu, N.; Turnage-Butterbaugh, C. Extremal primes for elliptic curves without complex multiplication, Proceedings of the American Mathematical Society, Volume 148 (2019) no. 3, p. 929 | DOI:10.1090/proc/14748
  • Illusie, Luc Pierre Deligne: A Poet of Arithmetic Geometry, The Abel Prize 2013-2017 (2019), p. 13 | DOI:10.1007/978-3-319-99028-6_2
  • Chiriac, Liubomir; Jorza, Andrei Comparing Hecke coefficients of automorphic representations, Transactions of the American Mathematical Society, Volume 372 (2019) no. 12, p. 8871 | DOI:10.1090/tran/7903
  • Charles, François Exceptional isogenies between reductions of pairs of elliptic curves, Duke Mathematical Journal, Volume 167 (2018) no. 11 | DOI:10.1215/00127094-2018-0011
  • Shotton, Jack The Breuil–Mézard conjecture when l≠p, Duke Mathematical Journal, Volume 167 (2018) no. 4 | DOI:10.1215/00127094-2017-0039
  • Arthur, James Functoriality and the Trace Formula, Geometric Aspects of the Trace Formula (2018), p. 1 | DOI:10.1007/978-3-319-94833-1_1
  • du Sautoy, Marcus Natural boundaries for Euler products of Igusa zeta functions of elliptic curves, International Journal of Number Theory, Volume 14 (2018) no. 08, p. 2317 | DOI:10.1142/s1793042118501415
  • Calegari, Frank; Geraghty, David Modularity lifting beyond the Taylor–Wiles method, Inventiones mathematicae, Volume 211 (2018) no. 1, p. 297 | DOI:10.1007/s00222-017-0749-x
  • Calegari, Frank Non-minimal modularity lifting in weight one, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018 (2018) no. 740, p. 41 | DOI:10.1515/crelle-2015-0071
  • de la Bretèche, Régis; Sha, Min; Shparlinski, Igor E.; Voloch, José Felipe The Sato–Tate distribution in thin parametric families of elliptic curves, Mathematische Zeitschrift, Volume 290 (2018) no. 3-4, p. 831 | DOI:10.1007/s00209-018-2042-0
  • Arthur, James Functoriality and the Trace Formula, Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms, Volume 2221 (2018), p. 319 | DOI:10.1007/978-3-319-95231-4_7
  • Herzig, Florian; Le, Daniel; Morra, Stefano On mod local-global compatibility for in the ordinary case, Compositio Mathematica, Volume 153 (2017) no. 11, p. 2215 | DOI:10.1112/s0010437x17007357
  • Clozel, Laurent; Thorne, Jack A. Level-raising and symmetric power functoriality, III, Duke Mathematical Journal, Volume 166 (2017) no. 2 | DOI:10.1215/00127094-3714971
  • Sha, Min; Shparlinski, Igor E. The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height, Indagationes Mathematicae, Volume 28 (2017) no. 2, p. 306 | DOI:10.1016/j.indag.2016.07.004
  • Wong, Peng-Jie A variant of Heilbronn characters, International Journal of Number Theory, Volume 13 (2017) no. 06, p. 1547 | DOI:10.1142/s1793042117500865
  • Choi, Suh Hyun Local universal lifting spaces of mod l Galois representations, Journal of Number Theory, Volume 176 (2017), p. 113 | DOI:10.1016/j.jnt.2016.12.006
  • Thorne, Jack A. A 2-adic automorphy lifting theorem for unitary groups over CM fields, Mathematische Zeitschrift, Volume 285 (2017) no. 1-2, p. 1 | DOI:10.1007/s00209-016-1681-2
  • Shotton, Jack Local deformation rings for GL2 and a Breuil–Mézard conjecture when l≠p, Algebra Number Theory, Volume 10 (2016) no. 7, p. 1437 | DOI:10.2140/ant.2016.10.1437
  • Buzzard, Kevin; Gee, Toby Slopes of Modular Forms, Families of Automorphic Forms and the Trace Formula (2016), p. 93 | DOI:10.1007/978-3-319-41424-9_2
  • Cha, Byungchul; Fiorilli, Daniel; Jouve, Florent Independence of the Zeros of Elliptic Curve L-Functions over Function Fields, International Mathematics Research Notices (2016), p. rnw087 | DOI:10.1093/imrn/rnw087
  • Sorensen, Claus M. The local Langlands correspondence in families and Ihara's lemma for U(n), Journal of Number Theory, Volume 164 (2016), p. 127 | DOI:10.1016/j.jnt.2015.12.012
  • James, Kevin; Tran, Brandon; Trinh, Minh-Tam; Wertheimer, Phil; Zantout, Dania Extremal primes for elliptic curves, Journal of Number Theory, Volume 164 (2016), p. 282 | DOI:10.1016/j.jnt.2016.01.009
  • Fiorilli, Daniel A conditional determination of the average rank of elliptic curves, Journal of the London Mathematical Society, Volume 94 (2016) no. 3, p. 767 | DOI:10.1112/jlms/jdw058
  • Harvey, David; Massierer, Maike; Sutherland, Andrew V. Computing -series of geometrically hyperelliptic curves of genus three, LMS Journal of Computation and Mathematics, Volume 19 (2016) no. A, p. 220 | DOI:10.1112/s1461157016000383
  • The Sato-Tate conjecture, Lectures on N_X(p) (2016), p. 111 | DOI:10.1201/b11315-11
  • Thorne, Jack A. Automorphy of some residually dihedral Galois representations, Mathematische Annalen, Volume 364 (2016) no. 1-2, p. 589 | DOI:10.1007/s00208-015-1214-z
  • Emerton, Matthew; Gee, Toby; Savitt, David Lattices in the cohomology of Shimura curves, Inventiones mathematicae, Volume 200 (2015) no. 1, p. 1 | DOI:10.1007/s00222-014-0517-0
  • Yamashita, Go; Yasuda, Seidai On some applications of integral p-adic Hodge theory to Galois representations, Journal of Number Theory, Volume 147 (2015), p. 721 | DOI:10.1016/j.jnt.2014.07.026
  • Chang, Alan; Mehrle, David; Miller, Steven J.; Reiter, Tomer; Stahl, Joseph; Yott, Dylan Newman's conjecture in function fields, Journal of Number Theory, Volume 157 (2015), p. 154 | DOI:10.1016/j.jnt.2015.04.028
  • Silverman, Joseph H.; Tate, John T. Cubic Curves over Finite Fields, Rational Points on Elliptic Curves (2015), p. 117 | DOI:10.1007/978-3-319-18588-0_4
  • Zywina, David The Sato-Tate law for Drinfeld modules, Transactions of the American Mathematical Society, Volume 368 (2015) no. 3, p. 2185 | DOI:10.1090/tran/6577
  • Barnet-Lamb, Thomas; Gee, Toby; Geraghty, David; Taylor, Richard Potential automorphy and change of weight, Annals of Mathematics, Volume 179 (2014) no. 2, p. 501 | DOI:10.4007/annals.2014.179.2.3
  • Buzzard, Kevin; Gee, Toby The conjectural connections between automorphic representations and Galois representations, Automorphic Forms and Galois Representations (2014), p. 135 | DOI:10.1017/cbo9781107446335.006
  • THORNE, JACK A. Raising the level for, Forum of Mathematics, Sigma, Volume 2 (2014) | DOI:10.1017/fms.2014.14
  • Harris, Michael Galois representations, automorphic forms, and the Sato-Tate Conjecture, Indian Journal of Pure and Applied Mathematics, Volume 45 (2014) no. 5, p. 707 | DOI:10.1007/s13226-014-0085-4
  • Fiorilli, Daniel Elliptic Curves of Unbounded Rank and Chebyshev's Bias, International Mathematics Research Notices, Volume 2014 (2014) no. 18, p. 4997 | DOI:10.1093/imrn/rnt103
  • Andrade, Julio; Chang, Alan; Miller, Steven J. Newman's conjecture in various settings, Journal of Number Theory, Volume 144 (2014), p. 70 | DOI:10.1016/j.jnt.2014.04.021
  • Blomer, Valentin; Brumley, Farrell The role of the Ramanujan conjecture in analytic number theory, Bulletin of the American Mathematical Society, Volume 50 (2013) no. 2, p. 267 | DOI:10.1090/s0273-0979-2013-01404-6
  • Katz, Nicholas M. Simple things we don’t know, Colloquium De Giorgi 2010–2012 (2013), p. 9 | DOI:10.1007/978-88-7642-457-1_2
  • Berger, Tobias; Klosin, Krzysztof On deformation rings of residually reducible Galois representations and R = T theorems, Mathematische Annalen, Volume 355 (2013) no. 2, p. 481 | DOI:10.1007/s00208-012-0793-1
  • Jones, Nathan Elliptic aliquot cycles of fixed length, Pacific Journal of Mathematics, Volume 263 (2013) no. 2, p. 353 | DOI:10.2140/pjm.2013.263.353
  • Murty, M. Ram; Murty, V. Kumar The Sato–Tate Conjecture for the Ramanujan τ-Function, The Mathematical Legacy of Srinivasa Ramanujan (2013), p. 155 | DOI:10.1007/978-81-322-0770-2_12
  • Gee, Toby; Geraghty, David Companion forms for unitary and symplectic groups, Duke Mathematical Journal, Volume 161 (2012) no. 2 | DOI:10.1215/00127094-1507376
  • Shparlinski, Igor E. Modular hyperbolas, Japanese Journal of Mathematics, Volume 7 (2012) no. 2, p. 235 | DOI:10.1007/s11537-012-1140-8
  • Thorne, Jack On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne, Journal of the Institute of Mathematics of Jussieu, Volume 11 (2012) no. 4, p. 855 | DOI:10.1017/s1474748012000023
  • Narkiewicz, Władysław The Last Period, Rational Number Theory in the 20th Century (2012), p. 307 | DOI:10.1007/978-0-85729-532-3_6
  • Guerberoff, Lucio Modularity lifting theorems for Galois representations of unitary type, Compositio Mathematica, Volume 147 (2011) no. 4, p. 1022 | DOI:10.1112/s0010437x10005154
  • Silverman, Joseph H.; Stange, Katherine E. Amicable Pairs and Aliquot Cycles for Elliptic Curves, Experimental Mathematics, Volume 20 (2011) no. 3, p. 329 | DOI:10.1080/10586458.2011.565253
  • HAESSIG, C. DOUGLAS; ROJAS-LEÓN, ANTONIO L-FUNCTIONS OF SYMMETRIC POWERS OF THE GENERALIZED AIRY FAMILY OF EXPONENTIAL SUMS, International Journal of Number Theory, Volume 07 (2011) no. 08, p. 2019 | DOI:10.1142/s1793042111005040
  • PANDE, AFTAB DEFORMATIONS OF GALOIS REPRESENTATIONS AND THE THEOREMS OF SATO–TATE AND LANG–TROTTER, International Journal of Number Theory, Volume 07 (2011) no. 08, p. 2065 | DOI:10.1142/s1793042111004939
  • Calegari, Frank Even Galois representations and the Fontaine–Mazur conjecture, Inventiones mathematicae, Volume 185 (2011) no. 1, p. 1 | DOI:10.1007/s00222-010-0297-0
  • Miller, Steven J.; Murty, M. Ram Effective equidistribution and the Sato–Tate law for families of elliptic curves, Journal of Number Theory, Volume 131 (2011) no. 1, p. 25 | DOI:10.1016/j.jnt.2010.06.013
  • Gee, Toby Automorphic lifts of prescribed types, Mathematische Annalen, Volume 350 (2011) no. 1, p. 107 | DOI:10.1007/s00208-010-0545-z
  • Harris, Michael; Shepherd-Barron, Nick; Taylor, Richard A family of Calabi-Yau varieties and potential automorphy, Annals of Mathematics, Volume 171 (2010) no. 2, p. 779 | DOI:10.4007/annals.2010.171.779
  • Qiu, Derong On some congruence properties of elliptic curves, Archiv der Mathematik, Volume 94 (2010) no. 2, p. 139 | DOI:10.1007/s00013-009-0100-x
  • Harris, Michael Arithmetic applications of the Langlands program, Japanese Journal of Mathematics, Volume 5 (2010) no. 1, p. 1 | DOI:10.1007/s11537-010-0945-6
  • Virdol, Cristian Potential modularity for elliptic curves and some applications, Journal of Number Theory, Volume 129 (2009) no. 12, p. 3109 | DOI:10.1016/j.jnt.2009.06.010
  • Virdol, Cristian On the Birch and Swinnerton-Dyer conjecture for elliptic curves over totally real number fields, Proceedings of the American Mathematical Society, Volume 137 (2009) no. 12, p. 4019 | DOI:10.1090/s0002-9939-09-10011-4

Cité par 107 documents. Sources : Crossref