speaker: Shinichi Kobayashi(Kyushu)

title: p-adic Aspects of the Coefficients of the Weierstrass Sigma Function

Abstract:

The coefficients of the Weierstrass sigma function of an elliptic curve are arithmetically significant. In the case of complex multiplication, they are related to special values of Hecke L-functions of imaginary quadratic fields and to anticyclotomic Iwasawa theory. For elliptic curves with ordinary reduction at a prime p, the p-adic properties of the sigma function are well understood, notably through the Mazur–Tate p-adic sigma function and its applications to p-adic height pairings. In contrast, for supersingular reduction at p, the speakers have established relations between the p-adic radius of convergence and p-adic periods.

In this talk, we explain these results and, time permitting, discuss further recent developments.