Canonical lifts and $δ$-structures

James Borger, Lance Gurney

Published 2019-05-25Version 1

We extend the Serre-Tate theory of canonical lifts of ordinary abelian varieties to arbitrary families of ordinary abelian varieties parameterised by a $p$-adic formal scheme $S$. We show that the canonical lift is the unique lift to $W(S)$ which admits a $\delta$-structure in the sense of Joyal and Buium.