Stephen Meagher (University of Groningen)

Friday 9th May, 12.05-12.55pm, Carslaw 373

Twists of genus three Jacobians

In this talk we we explain a conjecture of Serre on genus three curves over finite fields. We then describe a strategy for solving this conjecture via the use of Jacobian varieties and the Torelli theorem.

Unfortunately, this strategy fails to work due to the fact that Jacobians of genus three curves can have twists which are not themselves Jacobians. We explain how a Siegel modular form of degree on the Siegel upperhalf space of degree 3 can be used to distinguish between a Jacobian and its twist.