DERIVED HECKE ACTION AT p AND THE ORDINARY p-ADIC COHOMOLOGY OF ARITHMETIC MANIFOLDS

被引:0
作者
Khare, Chandrashekhar [1 ]
Ronchetti, Niccolo [1 ]
机构
[1] UCLA, Dept Math, Los Angeles, CA 90095 USA
关键词
POTENTIAL AUTOMORPHY; GALOIS; REPRESENTATIONS; DEFORMATIONS; THEOREMS; ALGEBRA;
D O I
10.1353/ajm.2023.a913294
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the derived Hecke action at p on the ordinary p-adic cohomology of arithmetic subgroups of reductive groups G(Q). This is the analog at l = p of derived Hecke actions studied by Venkatesh in the tame case, and is the derived analog of Hida's theory for ordinary Hecke algebras. We show that properties of the derived Hecke action at p are related to deep conjectures in Galois cohomology which are higher analogs of the classical Leopoldt conjecture.
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收藏
页码:1631 / 1694
页数:65
相关论文
共 34 条
[1]   Potential automorphy over CM fields [J].
Allen, Patrick B. ;
Calegari, Frank ;
Caraiani, Ana ;
Gee, Toby ;
Helm, David ;
Le Hung, Bao V. ;
Newton, James ;
Scholze, Peter ;
Taylor, Richard ;
Thorne, Jack A. .
ANNALS OF MATHEMATICS, 2023, 197 (03) :897-1113
[2]   DEFORMATIONS OF POLARIZED AUTOMORPHIC GALOIS REPRESENTATIONS AND ADJOINT SELMER GROUPS [J].
Allen, Patrick B. .
DUKE MATHEMATICAL JOURNAL, 2016, 165 (13) :2407-2460
[3]   Potential automorphy and change of weight [J].
Barnet-Lamb, Thomas ;
Gee, Toby ;
Geraghty, David ;
Taylor, Richard .
ANNALS OF MATHEMATICS, 2014, 179 (02) :501-609
[4]  
Bellache J., An introduction to the conjecture of Bloch and Kato
[5]  
Bloch S., 1990, Progr. Math., V86, P333
[6]  
Borel A., 2000, MATH SURVEYS MONOGRA, V67
[7]  
Buzzard K, 2014, LOND MATH S, V414, P135
[8]  
Calegari F., 2020, appendix to Duke Math, V169, P801
[9]   Modularity lifting beyond the Taylor-Wiles method [J].
Calegari, Frank ;
Geraghty, David .
INVENTIONES MATHEMATICAE, 2018, 211 (01) :297-433
[10]   Even Galois representations and the Fontaine-Mazur conjecture [J].
Calegari, Frank .
INVENTIONES MATHEMATICAE, 2011, 185 (01) :1-16