A general theory of canonical lifts

James Borger

ANU

Date:

Thu, 18/05/2017 - 2:00pm

Venue:

RC-4082, The Red Centre, UNSW

Abstract:

The classical theory of canonical lifts for elliptic curves gives a canonical way of lifting ordinary'' elliptic curves in positive characteristic to characteristic zero. I'll explain a new point of view on this which relies on a better understanding of the formal properties of the Witt vector construction. The formal nature of this approach suggests that it is the right framework for handling canonical lifts in general moduli problems. It also has a few pleasant consequences in the theory of canonical lifts of elliptic curves. The classical theory becomes nearly tautological, and it works for families of elliptic curves, rather than just individual ones. It even works for $p$-adic families, rather than just families in characteristic $p$. (This is joint work with Lance Gurney.)