Number Theory Seminar
An Euler system is a collection of norm-compatible first Galois cohomology classes with the Galois groups varying over cyclotomic fields. By constructing an Euler system, one can bound the Selmer group of Galois representations, though this is not easy in general. We construct Euler systems for the Galois representations coming from automorphic representations of GSp4×GL2. The strategy follows the work of Loeffler-Zerbes-Skinner in the case of GSp4, using automorphic input to show norm compatibility. This is a work in progress with Zhaorong Jin and Ryotaro Sakamoto.