Weil-étale cohomology and zeta-values of arithmetic schemes at negative integers

2021/02/24 by Beshenov, Alexey
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.12114

Abstract

Following the ideas of Flach and Morin (Doc. Math. 23 (2018), 1425--1560), we state a conjecture in terms of Weil-étale cohomology for the vanishing order and special value of the zeta function ζ(X, s) at s = n < 0, where X is a separated scheme of finite type over Spec ℤ. We prove that the conjecture is compatible with closed-open decompositions of schemes and with affine bundles, and consequently, that it holds for cellular schemes over certain one-dimensional bases. This is a continuation of arXiv:2012.11034, which gives a construction of Weil-étale cohomology for n < 0 under the mentioned assumptions on X.

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