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 Attachments

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