Université Lille 1



The eigencurve at classical weight one points


This is a joint work with Joël Bellaïche. We determine the geometry of the p-adic eigencurve at points corresponding to classical modular forms of weight one, under a mild assumption of regularity at p, and give several number theoretic applications. Namely we prove that the eigencurve is always smooth at those points, and that it is étale over the weight space if and only if the form does not have real multiplication by a real quadratic field in which p splits. Our approach uses deformation theory of Galois representations and the Baker–Brumer theorem in transcendence theory.


The Catalan Mathematical Society invites participants to this first congress of a biannual series focusing on current research topics across several areas of Mathematics.

Plenary talks and thematic sessions have been selected by the Scientific Committee of the SCM. Special thanks are due to the organisers of the thematic sessions and to the local mathematical community as a whole for their support to this congress.



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