On the eigencurve at classical weight 1 points

Joël Bellaïche; Mladen Dimitrov

doi:10.1215/00127094-3165755

Abstract

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.

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Joël Bellaïche. Mladen Dimitrov. "On the eigencurve at classical weight $1$ points." Duke Math. J. 165 (2) 245 - 266, 1 February 2016. https://doi.org/10.1215/00127094-3165755

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Received: 5 December 2012; Revised: 3 February 2015; Published: 1 February 2016

First available in Project Euclid: 19 January 2016

zbMATH: 06556667

MathSciNet: MR3457673

Digital Object Identifier: 10.1215/00127094-3165755

Subjects:

Primary: 11F33

Secondary: 11F11 , 11F80

Keywords: deformations of Galois representations , eigencurve , weight $1$ modular forms , weight one modular forms

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