Arithmetic Geometry and Number Theory RTG Seminar: Serre-Tate theory for Calabi-Yau varieties

Seminar | April 15 | 3-5 p.m. | 748 Evans Hall

 Piotr Achinger, IMPAN Warsaw and MSRI

 Department of Mathematics

Classical Serre-Tate theory concerns the deformation theory of ordinary abelian varieties. It implies that their deformation spaces can be equipped with a group structure and a lifting of the Frobenius morphism, and consequently such varieties admit a canonical lifting to characteristic zero. In the first half of the talk, aimed at graduate students and people with no prior exposure to the topic, I will review the classical results in this direction.

In the second half, I will show how to obtain similar results for ordinary Calabi-Yau varieties of arbitrary dimension. The main tools will be Frobenius splittings and Witt vectors of length two. This is joint work with Maciej Zdanowicz (EPFL).