The University of Arizona
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Delta-structures and canonical lifts in families

Algebraic Geometry Seminar

Delta-structures and canonical lifts in families
Series: Algebraic Geometry Seminar
Location: ENR2 S395
Presenter: James Borger, ANU

I'll explain recent joint work with Lance Gurney. We prove that any family of ordinary abelian varieties parameterised by a p-adic formal scheme S lifts to a unique family over W(S) which admits a delta-structure in the sense of Joyal, Buium, and Bousfield. In the case where S is the spectrum of a perfect field of characteristic p, this specialises to the classical result of Serre-Tate and Messing that every ordinary abelian variety over a perfect field k lifts to a unique one over the ring W(k) of Witt vectors together with a lift of Frobenius.