Federico Binda (Regensburg): Rigidity for relative 0-cycles

In this talk, we will present a relation between the classical Chow group of relative 0-cycles on a regular scheme X, projective and flat over an excellent Henselian discrete valuation ring A with perfect residue field k, and the so-called cohomological Chow group of zero cycles of the special fiber. If k algebraically closed and with finite coefficients (prime to the residue characteristic) these groups turn out to be isomorphic. This generalizes a previous argument due to Esnault-Kerz-Wittenberg to the case of regular models with arbitrary reduction. From this, one can re-prove in case of bad reduction that the étale cycle class map for relative 0-cycles with finite coefficients on X is an isomorphism, a result due to Saito and Sato in the case of semi-stable reduction. This is a joint work with Amalendu Krishna.