# Weil-\'etale cohomology and zeta-values of arithmetic schemes at negative integers

@inproceedings{Beshenov2021WeiletaleCA, title={Weil-\'etale cohomology and zeta-values of arithmetic schemes at negative integers}, author={Alexey Beshenov}, year={2021} }

Following the ideas of Flach and Morin [11], 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 SpecZ. 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 [2], which gives a…

## One Citation

Zeta-values of one-dimensional arithmetic schemes at strictly negative integers

- Mathematics
- 2021

Let X be an arithmetic scheme (i.e., separated, of finite type over SpecZ) of Krull dimension 1. For the associated zeta function ζ(X, s), we write down a formula for the special value at s = n < 0…

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