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 the cohomology theory, whereas
neither is periodic in general.
Lars Hesselholt
<larsh@math.nagoya-u.ac.jp>