Laboratoire Analyse, Géométrie et Applications

CNRSParis Citelogo-UP13-2

Colloquium du LAGA
Jeudi 19 janvier 15h30 - 16h30, Amphi Euler
Suivi du Thé du Laga en B407.

Prof. Lars Hesselholt (Nagoya/Copenhague)

Title: Topological Hochschild homology and the Hasse-Weil zeta function

Abstract: In the nineties, Deninger gave a detailed description of a
conjectural cohomological interpretation of the (completed) Hasse-Weil zeta
function of a regular scheme proper over the ring of rational integers. He
envisioned the cohomology theory to take values in countably infinite
dimensional complex vector spaces and the zeta function to emerge as the
regularized determinant of the infinitesimal generator of a Frobenius flow.
In this talk, I will explain that for a scheme smooth and proper over a
finite field, the desired cohomology theory naturally appears from the Tate
cohomology of the action by the circle group on the topological Hochschild
homology of the scheme in question.