Modularity of Galois Representations and Langlands Functoriality

被引:1
作者
Newton, James [1 ]
机构
[1] Univ Oxford, Math Inst, Oxford, England
关键词
EULER PRODUCTS; AUTOMORPHY; CONJECTURE; COHOMOLOGY; FORMS; CLASSIFICATION; TORSION; IMAGE;
D O I
10.1007/s41745-022-00305-0
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
This survey reports on some of the recent developments in the area of Galois representations and automorphic forms, with a particular focus on the author and Thorne's work on symmetric power functoriality for modular forms.
引用
收藏
页码:861 / 884
页数:24
相关论文
共 99 条
[1]  
Allen PB, 2022, Arxiv, DOI arXiv:1812.09999
[2]   Automorphy lifting for residually reducible l-adic Galois representations, II [J].
Allen, Patrick B. ;
Newton, James ;
Thorne, Jack A. .
COMPOSITIO MATHEMATICA, 2020, 156 (11) :2399-2422
[3]   DEFORMATIONS OF POLARIZED AUTOMORPHIC GALOIS REPRESENTATIONS AND ADJOINT SELMER GROUPS [J].
Allen, Patrick B. .
DUKE MATHEMATICAL JOURNAL, 2016, 165 (13) :2407-2460
[4]   RAISING THE LEVEL OF AUTOMORPHIC REPRESENTATIONS OF GL2n OF UNITARY TYPE [J].
Anastassiades, Christos ;
Thorne, Jack A. .
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2022, 21 (04) :1421-1444
[5]  
[Anonymous], 1964, Publ. Math. Inst. Hautes Etudes Sci.
[6]   GALOIS REPRESENTATIONS ATTACHED TO MOD-P COHOMOLOGY OF GL(N,Z) [J].
ASH, A .
DUKE MATHEMATICAL JOURNAL, 1992, 65 (02) :235-255
[7]   Potential automorphy and change of weight [J].
Barnet-Lamb, Thomas ;
Gee, Toby ;
Geraghty, David ;
Taylor, Richard .
ANNALS OF MATHEMATICS, 2014, 179 (02) :501-609
[8]   THE SATO-TATE CONJECTURE FOR HILBERT MODULAR FORMS [J].
Barnet-Lamb, Thomas ;
Gee, Toby ;
Geraghty, David .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 24 (02) :411-469
[9]   A Family of Calabi-Yau Varieties and Potential Automorphy II [J].
Barnet-Lamb, Tom ;
Geraghty, David ;
Harris, Michael ;
Taylor, Richard .
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2011, 47 (01) :29-98
[10]  
Bellaïche J, 2009, ASTERISQUE, P1