Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation

• 成果类型: Article
• 署名作者: Kings, Guido; Sprang, Johannes
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2025.202.1.1
• 发表日期: 2025
• 页码: 1-109
• 关键词: cocycles

摘要

We show that for an arbitrary totally complex number field L the (regularized) critical L-values of algebraic Hecke characters of L divided by certain periods are algebraic integers. This relies on a new construction of an equivariant coherent cohomology class with values in the completion of the Poincare bundle on an abelian scheme A. From this we obtain a cohomology class for the automorphism group of a CM abelian scheme A with values in some canonical bundles, which can be explicitly calculated in terms of Eisenstein-Kronecker series. As a further consequence, using an infinitesimal trivialization of the Poincare bundle, we construct a p-adic measure interpolating the critical L-values in the ordinary case. This generalizes previous results for CM fields by Damerell, Shimura and Katz and settles the algebraicity and p-adic interpolation in the remaining open cases of critical values of Hecke L-functions.