Euler systems for Hilbert modular surfaces

Antonio Lei, David Loeffler, Sarah Livia Zerbes

Published 2016-07-26Version 1

We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Beilinson on injectivity of regulator maps holds, this Euler system is non-trivial, and we deduce bounds towards the Iwasawa main conjecture for these Galois representations.