Big image of Galois representations associated with finite slope $p$-adic families of modular forms

Andrea Conti (1) , Adrian Iovita (2, 3) , Jacques Tilouine (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Department of Mathematics and Statistics,Concordia University
3 Dipartimento di Matematica [padova]

We consider the Galois representation associated with a finite slope $p$-adic family of modular forms. We prove that the Lie algebra of its image contains a congruence Lie subalgebra of a non-trivial level. We describe the largest such level in terms of the congruences of the family with $p$-adic CM forms.

Mots clés: p-adic modular forms; Galois representations; Relative Sen theory; p-adic CM forms; Congruences; Eigencurve; Big Galois image

Domaines: Théorie des nombres [math.NT]

Andrea Conti, Adrian Iovita, Jacques Tilouine. Big image of Galois representations associated with finite slope $p$-adic families of modular forms. 2015. ⟨hal-01183284v2⟩