Number Theory Seminar

Speaker: Aleksandre Maksoud

Title: The geometry of the eigencurve at classical weight one modular forms

Abstract: The study of p-adic deformations of automorphic forms was initiated by Hida
in the 1980s, after he discovered the existence of systematic congruences
between the Fourier coefficients of modular forms. The eigencurve is a
geometric incarnation of these congruences, introduced by Coleman and
Mazur, which is proving to be a fundamental tool in the study of
number-theoretic conjectures such as the Birch and Swinnerton-Dyer
conjecture.
In this talk, I will explain a new method for studying the geometry of the
eigencurve in the neighbourhood of weight 1 forms in a case where the
classical R=T arguments fall short. I will also discuss potential
applications to the BSD conjecture.
This is a joint work with Adel Betina and Alice Pozzi.

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