Number Theory Seminar

We give a conjectural description of Zeta-values of arithmetic schemes at $s=n$ for any integer $n\in\mathbb{Z}$, in terms of two perfect complexes of abelian groups. The first complex is called Weil-étale cohomology with compact support. The second complex can be thought of as derived de Rham cohomology modulo the Hodge filtration relatively to the sphere spectrum, and is defined using topological Hochschild homology. If time permits, we will state a similar formula for a certain product of Gamma-factors. It is joint work with Matthias Flach.