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

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 $\zeta (X,s)$ at $s=n<0$, where $X$ is a separated scheme of finite type over $\mathrm{Spec}\mathbb{Z}$. 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 $X$.

The new title is "Weil-étale cohomology and zeta-values of arithmetic schemes at negative integers". Minor improvements in presentation. Updated references to arXiv:2012.11034

References in corpus (1)

• The Abel-Jacobi Map for Higher Chow Groups, II

Cited by in corpus (1)

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