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

Andrea Conti; Adrian Iovita; Jacques Tilouine

doi:10.1007/978-3-319-45032-2

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arXiv · 1508.01598

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

Andrea Conti·Adrian Iovita·Jacques Tilouine

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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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Andrea Conti, Adrian Iovita, Jacques Tilouine. 2016-12-08. Big image of Galois representations associated with finite slope $p$-adic families of modular forms. https://doi.org/10.1007/978-3-319-45032-2

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