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 prove that the Lie algebra of the image of the Galois representation associated with a finite slope family of modular forms contains a congruence subalgebra of a certain level. We interpret this level in terms of congruences with CM forms.

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-01183284v1⟩