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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01183284
Contributor : Andrea Conti <>
Submitted on : Saturday, December 10, 2016 - 5:03:26 PM
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Andrea Conti, Adrian Iovita, Jacques Tilouine. Big image of Galois representations associated with finite slope $p$-adic families of modular forms. 2015. ⟨hal-01183284v2⟩

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