Title: Computation of p-torsion of Jacobians of hyperelliptic curves
Abstract: An elliptic curve defined over a finite field of characteristic p can be ordinary or supersingular; this distinction measures certain properties of its p-torsion. The p-torsion of the Jacobian of a curve of higher genus can also be studied and classified by interesting combinatorial invariants, such as the p-rank, a-number, and Ekedahl-Oort type. Algorithms to compute these invariants exist but have not been implemented. In this talk, I will explain how to compute these invariants and describe the lag in producing explicit curves with given p-torsion invariants.