1,193 research outputs found
Topological Hochschild homology and the Hasse-Weil zeta function
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
- …