Étale and Motivic Homotopy Theory

We introduce relative motivic complex as a complex of Zariski sheaves on X for a pair (X;D) of a smooth variety and an eective (non-reduced) Cartier divisor. Its cohomology groups called relative motivic cohomology are related to various non-homotopy invariants such as relative Picard groups, relative Chow groups with moduli, and additive higher Chow groups by Bloch{Esnault{Park. The main results are computation of the motivic complex in weight one, and computation of relative motivic cohomology using relative Milnor K-groups, and the construction of regulator maps to a relative version of Deligne cohomology, which provides Abel{Jacobi maps with additive parts.

Dienstag, den 25. März 2014 um 09.30-10.30 Uhr, in INF288, HS2 Dienstag, den 25. März 2014 at 09.30-10.30, in INF288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Alexander Schmidt, Jakob Stix