Topological Hochschild homology and the Hasse-Weil zeta function
Number Theory
2019-07-18 v2 K-Theory and Homology
Abstract
We consider the Tate cohomology of the circle group acting on the topological Hochschild homology of schemes. We show that in the case of a scheme smooth and proper over a finite field, this cohomology theory naturally gives rise to the cohomological interpretation of the Hasse-Weil zeta function by regularized determinants envisioned by Deninger. In this case, the periodicity of the zeta function is reflected by the periodicity of said cohomology theory, whereas neither is periodic in general.
Keywords
Cite
@article{arxiv.1602.01980,
title = {Topological Hochschild homology and the Hasse-Weil zeta function},
author = {Lars Hesselholt},
journal= {arXiv preprint arXiv:1602.01980},
year = {2019}
}