Weil-etale cohomology and special values of L-functions at zero

2016/08/03 by Minh-Hoang Tran, Tran, Minh-Hoang
Mathematics · #11R29 (Secondary) #11R34 #11S40 #14F20 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1608.01152

openalex publication_date 2016/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct the Weil-étale cohomology and Euler characteristics for a subclass of the class of ℤ-constructible sheaves on the spectrum of the ring of integers of a totally imaginary number field. Then we show that the special value of an Artin L-function of toric type at zero is given by the Weil-étale Euler characteristic of an appropriate ℤ-constructible sheaf up to signs. As applications of our result, we will derive some classical formulas of special values of L-functions of tori and their class numbers.

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