虚二次域上GL N的爱森斯坦上同类

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-05 DOI:10.1515/crelle-2022-0089

N. Bergeron, Pierre Charollois, Luis E. García

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引用次数: 3

摘要

摘要研究了虚二次域k上局部对称空间GL N {\ mathm {GL}_{N}}的N-1 {N-1}次Eisenstein上同调类的算法。在自然条件下，我们将这些类在N次扩展L/k {L/k}相关的(N-1) {(N-1)}环上作为广义Dedekind和的线性组合求值。因此，我们证明了schzech和Colmez的一个重要猜想，将L的Hecke特征上的L函数的临界值表示为Kronecker-Eisenstein级数的多项式，在椭圆曲线的扭转点上用复数乘以k来求值。我们特别恢复了这些临界值的代数性。

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Eisenstein cohomology classes for GL N over imaginary quadratic fields

Abstract We study the arithmetic of degree N - 1 {N-1} Eisenstein cohomology classes for the locally symmetric spaces attached to GL N {\mathrm{GL}_{N}} over an imaginary quadratic field k. Under natural conditions we evaluate these classes on ( N - 1 ) {(N-1)} -cycles associated to degree N extensions L / k {L/k} as linear combinations of generalized Dedekind sums. As a consequence we prove a remarkable conjecture of Sczech and Colmez expressing critical values of L-functions attached to Hecke characters of L as polynomials in Kronecker–Eisenstein series evaluated at torsion points on elliptic curves with complex multiplication by k. We recover in particular the algebraicity of these critical values.

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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.