EULER SYSTEMS FOR HILBERT MODULAR SURFACES. (15th November 2018) - LEI, ANTONIO; LOEFFLER, DAVID; ZERBES, SARAH LIVIA
Abstract : 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 Bloch and Kato on injectivity of regulator maps holds, this Euler system is nontrivial, and we deduce bounds towards the Iwasawa main conjecture for these Galois representations.