Morningside Center of Mathematics

Chinese Academy of Sciences

中国科学院晨兴数学中心

Morningside Center of Mathematics

Chinese Academy of Sciences

Title: | Duality of Drinfeld Modules and P-adic Properties of Drinfeld Modular Forms |

Speaker: | Shin Hattori (Tokyo City University) |

Time: | 2019-6-5, 16:30-17:30 |

Place: | 110 |

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 v-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. |

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