推导了算术流形在p点的Hecke作用和普通p进上同调

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-29 DOI:10.1353/ajm.2023.a913294

Chandrashekhar Khare, Niccoló Ronchetti

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引用次数: 0

摘要

摘要研究了约化群${\rm G}(\Bbb{Q})$的算术子群$p$-进上同调上$p$处的推导Hecke作用。这是Venkatesh在温顺的情况下研究的推导出的Hecke作用在$\ well =p$处的类比，也是Hida的理论对普通Hecke代数的推导出的类比。我们证明了在$p$处推导出的Hecke作用的性质与伽罗瓦上同调中的深度猜想有关，这是经典利奥波德猜想的高级类比。

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Derived Hecke action at p and the ordinary p-adic cohomology of arithmetic manifolds

Abstract:

We study the derived Hecke action at $p$ on the ordinary $p$-adic cohomology of arithmetic subgroups of reductive groups ${\rm G}(\Bbb{Q})$. This is the analog at $\ell=p$ 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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.