Southern California Number Theory Day

Abstracts

Jacques Tilouine

Low weight degree four Galois representations and Siegel modular forms

Abstract: We show that certain abelian surfaces come from p-adic Siegel cusp forms (in the sense that they have the same p-adic Galois representation). This relates to the question: unless it is isogenous to a product of elliptic curves, does an abelian surface come from a Siegel cusp form?