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#### Seminar des SFB/TRR 326 GAUS

„Topological Hochschild homology and Zeta-values“
Prof. Dr. Baptiste Morin, Universität Bordeaux

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 motivic 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. The functional equation of Zeta functions together with our description of Zeta-values implies a formula relating these complexes, special values of the archimedean Euler factors and Bloch's conductor. We will state this formula, which can actually be proven. This is joint work with Matthias Flach. Meeting-Link $\underline{Meeting-Kennnummer (Zugriffscode):}$ 2730 494 4905 \$\underline{Meeting Passwort:} SFB326

Freitag, den 14. Januar 2022 um 13:30 Uhr, in Online (Webex), Freitag, den 14. Januar 2022 at 13:30, in Online (Webex),

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. A. Schmidt