The eigencurve at Eisenstein weight one points

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• Alice Pozzi (UCL)
• Tuesday 28 May 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Beth Romano.

In this talk, we discuss the geometry of the Coleman-Mazur eigencurve at weight one Eisenstein points. The local nature of the eigencurve is mostly un- derstood at classical points of weight greater than one, while one observes some unusual behaviours at weight one. In particular, we study cuspidal Hida families specializing to Eisenstein series at weight one. Our approach consists in studying the deformation rings of certain (deceptively simple!) Artin representations. We discuss the implications of our analysis on the classicality of a certain overconvergent eigenspace. Finally, we explain how this Galois-theoretic method yields some new insight on Gross’s formula relating the leading term of the p- adic L-function to a Stark unit. This is joint work with Adel Betina and Mladen Dimitrov.

This talk is part of the Number Theory Seminar series.

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