Time: 2019.09.18 17:00 ~ 18:30

Place: 404 Math building

Title: Generalizing p-adic sigma functions to abelian surfaces

Abstract : The Weierstrass sigma function is a complex analytic function associated to a lattice L inside the complex numbers and encodes much information about the elliptic curve E=C/L. In the late '80s Mazur and Tate developed a p-adic theory of a sigma function attached to an elliptic curve E defined over the p-adic numbers, when E has ordinary reduction. In this talk, we will recount the Mazur-Tate story and talk about what to expect when looking for higher dimensional generalizations. In particular we will discuss arithmetic on curves of genus two and their Jacobians in some detail.