TITLE: Higher dimensional p-adic CM construction.
ABSTRACT: I will discuss p-adic methods for the construction of curves over
number fields whose Jacobian has complex multiplication (CM) and for the
computation of zeta functions of abelian varieties over finite fields. My
focus is on higher dimensional methods based on the computation of theta
constants. A p-adic CM algorithm typically has as input an ordinary abelian
variety over a finite field of characteristic p and as output an
arithmetic invariant of the canonical lift over a p-adic ring. My talk
includes recent results by Gaudry, Houtman, Kohel, Lercier, Lubicz, Mestre,
Ritzenthaler, Weng and myself
.