Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series MATH-IHES
Subjects math
Date Wednesday 5 June 2019
Time 10:30
Institute IHES
Seminar Room Centre de conférences Marilyn et James Simons
Speaker's Last Name Hattori
Speaker's First Name Shin
Speaker's Email Address
Speaker's Institution Tokyo City University
Title Duality of Drinfeld Modules and P-adic Properties of Drinfeld Modular Forms
Abstract Let p be a rational prime, q>1 a p-power and P a non-constant irreducible polynomial in F_q[t]. The notion of Drinfeld modular form is an analogue over F_q(t) of that of elliptic modular form. Numerical computations suggest that Drinfeld modular forms enjoy some P-adic structures comparable to the elliptic analogue, while at present their P-adic properties are less well understood than the p-adic elliptic case. In 1990s, Taguchi established duality theories for Drinfeld modules and also for a certain class of finite flat group schemes called finite $\nu$-modules. Using the duality for the latter, we can define a function field analogue of the Hodge-Tate map. In this talk, I will explain how the Taguchi's theory and our Hodge-Tate map yield results on Drinfeld modular forms which are classical to elliptic modular forms e.g. P-adic congruences of Fourier coefficients imply p-adic congruences of weights.
arXiv Preprint Number
Comments Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo

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