Status  Confirmed 
Seminar Series  MATHIHES 
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 Padic Properties of Drinfeld Modular Forms 
Abstract  Let p be a rational prime, q>1 a ppower and P a nonconstant 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 Padic structures comparable to the elliptic analogue, while at present their Padic properties are less well understood than the padic 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 HodgeTate map. In this talk, I will explain how the Taguchi's theory and our HodgeTate map yield results on Drinfeld modular forms which are classical to elliptic modular forms e.g. Padic congruences of Fourier coefficients imply padic congruences of weights. 
arXiv Preprint Number  
Comments  Séminaire de Géométrie Arithmétique ParisPékinTokyo 
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