"Deforming endomorphisms of abelian varieties and arithmetic
applications"

Abstract: Given an abelian variety A over a finite field F, we consider
the problem of which endomorphisms of A extend to a deformation of A to
an artinian ring with residue field F. The problem is motivated by
recent work by the speaker and K. Lauter on constructing units in
abelian extensions of CM fields by means of special values of modular
functions. While I shall report briefly on this motivation and the
application, due to time limitation I shall focus on the particular
deformation problem.