James Borger (Australian National University)

Friday 9th March, 12.05-12.55pm, Carslaw 375 (***NEW ROOM***)

Basic geometry of the Witt vectors

The ring of Witt vectors (with entries in another ring) is an explicit construction in commutative algebra which has been used most often as a machine for lifting questions from prime characteristic to characteristic zero. But even many people who use it regard it as a mysterious formal device that doesn't really fit well with normal commutative algebra and algebraic geometry.

In this talk, I'll discuss the algebraic geometry of rings of Witt vectors and related constructions. For example, if we have a variety defined over a ring of integers R in a global field, I'll describe its variety of Witt vectors taken with respect to R. I'll also discuss some properties related to the étale topology. Some of them extend results of Illusie and of Langer-Zink.