On Euler systems for adjoint Hilbert modular Galois representations

TL;DR

This paper constructs Euler systems for adjoint Hilbert modular Galois representations using deformation theory and relates them to p-adic L-functions under a conjectural framework, advancing understanding in number theory.

Contribution

It introduces a method to produce Euler systems for adjoint Galois representations associated with Hilbert modular forms, linking them to p-adic L-functions and Fitting ideals.

Findings

Existence of Euler systems for adjoint Hilbert modular Galois representations.

Connection between Euler systems and p-adic L-functions under a conjectural formula.

Relation of these constructions to equivariant congruence modules for abelian base change.

Abstract

We prove the existence of Euler systems for adjoint modular Galois representations using deformations of Galois representations coming from Hilbert modular forms and relate them to $p$-adic $L$-functions under a conjectural formula for the Fitting ideals of some equivariant congruence modules for abelian base change.