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On the eigencurve at classical weight 1 points. (English) Zbl 1404.11047

Summary: We show that the \(p\)-adic eigencurve is smooth at classical weight \(1\) points which are regular at \(p\) and give a precise criterion for étaleness over the weight space at those points. Our approach uses deformations of Galois representations.

MSC:

11F33 Congruences for modular and \(p\)-adic modular forms
11F11 Holomorphic modular forms of integral weight
11F80 Galois representations
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References:

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