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Big image of Galois representations associated with finite slope \(p\)-adic families of modular forms. (English) Zbl 1416.11071

Loeffler, David (ed.) et al., Elliptic curves, modular forms and Iwasawa theory. In honour of John H. Coates’ 70th birthday, Cambridge, UK, March 2015. Proceedings of the conference and the workshop. Cham: Springer. Springer Proc. Math. Stat. 188, 87-123 (2016).
Summary: 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.
For the entire collection see [Zbl 1364.11005].

MSC:

11F80 Galois representations
11F85 \(p\)-adic theory, local fields
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