# Lars Hesselholt (Copenhagen, Nagoya): Topological Hochschild homology and the Hasse-Weil zeta function

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.
Published Sep. 27, 2017 11:44 AM
- Last modified Sep. 27, 2017 11:44 AM