On the Eigencurve at classical weight one points

Abstract

We show that the p-adic Eigencurve is smooth at classical weight one points which are regular at p and give a precise criterion for etaleness over the weight space at those points. Our approach uses deformations of Galois representations.

22 pages (revised version)

Cited by in corpus (6)

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• Arithmetic of critical $p$-adic $L$-functions
• On the $\mathcal{L}$-invariant of the adjoint of a weight one modular form