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SUMMARY:The eigencurve at Eisenstein weight one points - Alice Pozzi (UCL)
DTSTART:20190528T133000Z
DTEND:20190528T143000Z
UID:TALK123508@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:In this talk\, we discuss the geometry of the Coleman-Mazur ei
 gencurve at\nweight one Eisenstein points. The local nature of the eigencu
 rve is mostly un-\nderstood at classical points of weight greater than one
 \, while one observes some\nunusual behaviours at weight one. In particula
 r\, we study cuspidal Hida families\nspecializing to Eisenstein series at 
 weight one. Our approach consists in studying\nthe deformation rings of ce
 rtain (deceptively simple!) Artin representations.\nWe discuss the implica
 tions of our analysis on the classicality of a certain\noverconvergent eig
 enspace. Finally\, we explain how this Galois-theoretic method\nyields som
 e new insight on Gross’s formula relating the leading term of the p-\nad
 ic L-function to a Stark unit. This is joint work with Adel Betina and Mla
 den\nDimitrov.\n
LOCATION:MR13
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