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Global Methods in the Langlands Program


Cuspidal cohomology of stacks of shtukas

Author(s): Cong Xue
Published in: Compositio Mathematica, Issue 156/6, 2020, Page(s) 1079-1151, ISSN 0010-437X
DOI: 10.1112/s0010437x20007058


Author(s): Christos Anastassiades, Jack A. Thorne
Published in: Journal of the Institute of Mathematics of Jussieu, 2021, Page(s) 1-24, ISSN 1474-7480
DOI: 10.1017/s1474748020000602

On central extensions and simply laced Lie algebras

Author(s): Beth Romano
Published in: Journal of Algebra, Issue 568, 2021, Page(s) 480-511, ISSN 0021-8693
DOI: 10.1016/j.jalgebra.2020.09.046

Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications

Author(s): Cong Xue
Published in: Épijournal de Géométrie Algébrique, Issue Volume 4, 2020, ISSN 2491-6765
DOI: 10.46298/epiga.2020.volume4.5550

$\hat{G}$-local systems on smooth projective curves are potentially automorphic

Author(s): Gebhard Böckle, Michael Harris, Chandrashekhar Khare, Jack A. Thorne
Published in: Acta Mathematica, Issue 223/1, 2019, Page(s) 1-111, ISSN 0001-5962
DOI: 10.4310/acta.2019.v223.n1.a1

On the average number of 2-Selmer elements of elliptic curves over F_q(X) with two marked points

Author(s): Jack A. Thorne
Published in: Documenta Mathematica, 2019, ISSN 1431-0635
DOI: 10.25537/dm.2019v24.1179-1223

Modularity of PGL 2 ( p )-representations over totally real fields

Author(s): Patrick B. Allen, Chandrashekhar B. Khare, Jack A. Thorne
Published in: Proceedings of the National Academy of Sciences, Issue 118/33, 2021, Page(s) e2108064118, ISSN 0027-8424
DOI: 10.1073/pnas.2108064118

E8 and the average size of the 3‐Selmer group of the Jacobian of a pointed genus‐2 curve

Author(s): Beth Romano; Jack A. Thorne
Published in: Proceedings of the London Mathematical Society, 2020, ISSN 1460-244X
DOI: 10.17863/cam.58186

Automorphy lifting for residually reducible -adic Galois representations, II

Author(s): Patrick B. Allen, James Newton, Jack A. Thorne
Published in: Compositio Mathematica, Issue 156/11, 2020, Page(s) 2399-2422, ISSN 0010-437X
DOI: 10.1112/s0010437x20007484

Proceedings of the International Congress of Mathematicians 2018 (ICM 2018)

Author(s): Boyan Sirakov, Paulo Ney de Souza, Marcelo Viana
Published in: Potential automorphy of Ĝ-local systems, Issue 2018, 2018, Page(s) Vol. II, pp. 415--434
DOI: 10.1142/11060

On subquotients of the etale cohomology of Shimura varieties

Author(s): Johansson, Christian; Thorne, Jack A.
Published in: """Shimura Varieties"" in London Mathematical Society Lecture Note Series", Issue 457, 2020