Let p be a prime number, and let A be an abelian variety
over a finite field k of characteristic p. Let A[p] be
the p-torsion of A. As an abstract group this equals
(Z/pZ)^n for some n, but as a group scheme it can exhibit
interesting infinitesimal structures.
The goal of this talk is to answer the following question:
"given the field k and the integer dim(A), how many
isomorphism classes of A[p] exist?" We will show that
this question is best discussed in the context of
algebraic stacks, where we can answer this question
using the language of linear algebraic groups.