Columbia Algebraic Geometry Seminar

Speaker: Matthew Morrow

Title: “The deformation of algebraic cycles in characteristic p ”

Abstract: The problem of deforming vector bundles or algebraic cycles has classically been relatively well understood (at least conjecturally) in characteristic zero, and to a lesser extent in mixed characteristic, whereas the situation in equal characteristic p has been less satisfactory. I will explain a new theory of infinitesimal crystalline cycle classes in characteristic p, which allows general results of the following form to the proved: given an algebraic cycle on a subvariety Y of a variety X in characteristic p, the cycle extends to the formal completion of X along Y if and only if its crystalline cycle class extends. This leads to generalisations of results of de Jong, infinitesimal Lefschetz theorems, and a characteristic p analogue of the Deformational Hodge Conjectures introduced by Bloch-Esnault-Kerz.