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

2004/05/21 by Joël Bellaïche, Joel Bellaiche, Bellaiche, Joel +3 · 1 citation
Mathematics · #11F #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F

paper · pdf · doi:10.48550/arxiv.math/0405415

14 pages, LaTeX, french (second version: extended introduction, minor improvements)

openalex publication_date 2004/05/21 · arxiv created 2004/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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