Title: Euler systems and p-adic L-functions for GSp(4)

Abstract: Euler systems are compatible families of Galois cohomology classes attached to a global Galois representation, and they play an important role in proving cases of the Bloch—Kato conjecture. In my talk, I will explain the construction both of an Euler system and of a p-adic L-function attached to the spin representation of a genus 2 Siegel modular form. I will also sketch a strategy for proving an explicit reciprocity law, relating the bottom class of the Euler system to values of the p-adic L-function. This is work in progress with David Loeffler, Vincent Pilloni and Chris Skinner.