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Lissite de la courbe de Hecke de GL(2) aux points Eisenstein critiques

Joel Bellaiche·Gaetan Chenevier
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Abstract

Let p be a prime number and C be the p-adic tame level 1 eigencurve introduced by Coleman-Mazur. We prove that C is smooth at the evil Eisenstein points and we give necessary and sufficient conditions for etaleness of the map to the weight space at these points in terms of p-adic zeta values. A key step is the determination at these points of the schematic reducibility locus of the pseudo-character carried by C restricted to a decomposition group at p. Then, the smoothness appears to be a consequence of the fact that the Dirichlet L-functions only have simple zeros at integers.

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Joel Bellaiche, Gaetan Chenevier. 2004-06-17. Lissite de la courbe de Hecke de GL(2) aux points Eisenstein critiques. https://arxiv.org/abs/math/0405415

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