p-Torsion of Abelian varieties in characteristic p

Abstract: Let A be an Abelian variety of dimension g over an algebraically closed field k. We are interested in the group scheme A[p], consisting of the elements of A whose order divides p. If the characteristic of k is not p, then there is only one possibility for A[p]: as a group it consists of 2g copies of Z/pZ. On the other hand, if k has characteristic p, then there are several distinct possibilities for A[p], called Ekedahl-Oort strata. In particular, the group will consist of at most g copies of Z/pZ. An example of an Ekedahl-Oort stratification is the distinction between ordinary and supersingular elliptic curves. If the dimension g is higher, it is natural to ask which Ekedahl-Oort strata arise from the Jacobian of a curve. In this talk, we treat both previously known results and new results in this area. In many cases, we add the restriction that the curves in question are Artin-Schreier covers.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar