Conference website: https://sites.google.com/view/mispb2018/home
Title: “Rigidity for cycles of relative dimension zero”
Abstract: In this talk, we will present a relation between a certain group of algebraic cycles, with finite coefficients, on a regular quasi-projective scheme X, flat over an excellent Henselian DVR A with perfect residue field, and the motivic cohomology (with compact support) of the special fiber, in the range classically corresponding to the group of zero cycles and under the assumption of the existence of a good compactification of X.
When X is projective over A, this relation was studied by Bloch and Esnault-Kerz-Wittenberg, generalizing previous works by Sato and Saito. Our main result can be interpreted as a proper base change theorem ”with compact support” for relative 0-cycles. This is a joint work with Amalendu Krishna