On p-adic L-functions for Hilbert modular forms

Mardi 14 mars 2017 14:15-15:15 - John Bergdall - Boston University

Résumé : Analytic p-adic L-functions encode algebraic special values of L-functions classically associated to automorphic forms, say. They naturally arise in p-adic approaches to conjectures like that of Birch and Swinnerton-Dyer. Stevens developed an approach to their construction in the case of modular forms during the 1990’s. He verified his approach worked in « small slope » cases and, later, Pollack-Stevens and Bellaïche filled in the missing cases. The goal of this talk is to explain one aspect of generalizing these works to Hilbert modular forms. Specifically, we study distribution-valued cohomology spaces and give a sufficient condition under which we can associate unique, up to scalar, eigenclasses to classical (p-refined) Hilbert modular forms. The novelty of our result is that we do not include a « small slope » condition. Our proof makes crucial use of a p-adic family of Hilbert modular forms. This is joint with David Hansen.

Lieu : Bât. 425, salle 117-119

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