DERIVED HECKE ALGEBRA AND COHOMOLOGY OF ARITHMETIC GROUPS

被引：11

作者：

Venkatesh, Akshay ^{[1
]}

机构：

[1] Inst Adv Study, Olden Lane, Princeton, NJ 08540 USA

来源：

FORUM OF MATHEMATICS PI | 2019年 / 7卷

基金：

美国国家科学基金会;

关键词：

K-THEORY; REPRESENTATIONS;

D O I：

10.1017/fmp.2019.6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group Gamma. Under favorable conditions, the cohomology is freely generated in a single degree over this graded Hecke algebra. From this construction we extract an action of certain p-adic Galois cohomology groups on H* (Gamma, Q(p)), and formulate the central conjecture: the motivic Q-lattice inside these Galois cohomology groups preserves H*(Gamma, Q).

引用

页数：119

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