Southern California Number Theory Day

Biology and Mechanics: Applications of Math. and Computation
WEBSITE: http://www.math.uci.edu/~qnie/2006.html

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?