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

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

2004-05-21

arxiv.org/abs/math/0405415v2

Mathematics

Number Theory

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

Scientific paper

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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