Algebra/Topology seminar

Speaker: Dario Beraldo

Title: Proof of the Deligne-Milnor conjecture

Abstract: Let X --> S be a family of algebraic varieties parametrized by an infinitesimal disk S, possibly of mixed characteristic. The Bloch conductor conjecture expresses the difference of the Euler characteristics of the special and generic fibers in algebraic and arithmetic terms. I'll describe a proof of some new cases of this conjecture, including the case of isolated singularities. The latter was a conjecture of Deligne generalizing Milnor's formula on vanishing cycles. (This is joint work with Massimo Pippi.)

The first half of the talk is aimed at a general audience and many of the relevant objects will be introduced through examples.