Eisenstein cohomology classes for GL N over imaginary quadratic fields

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

引用次数: 3

Abstract

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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虚二次域上GL N的爱森斯坦上同类

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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