Beijing Institute of Mathematical Sciences and Applications

In this short course, I will provide a construction of certain p-adic L-functions attached to Siegel cusp forms of genus 2. Using explicit reciprocity laws, I will show how their non-vanishing implies the existence of non-vanishing Selmer classes. This gives evidence for conjectural formulas relating rational points of abelian surfaces to special values
The course is based on joint work in progress with Massimo Bertolini, M. Seveso and R. Venerucci.