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Number Theory Seminar

Thursday, March 14, 2019
4:00pm to 5:00pm
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Linde Hall 387
Drinfeld Modular Varieties for GL(r) and Families of Modular Forms
Marc-Hubert Nicole, Mathematical Institute of Marseille, Univ. d'Aix-Marseille,

Classical modular curves associated with GL(2) are moduli spaces of elliptic curves with additional structure. While there are no Shimura varieties associated with the general linear group GL( r) for r >2,the situation is sharply different over function fields. The Drinfeld modular variety for GL( r) is the moduli space of Drinfeld modules of rank r (with auxiliary level structure). It is a smooth, affine scheme of relative dimension r−1. I will recall how various analogues of well-established tools in the classical context extend to Drinfeld modular varieties and their modular forms: the Hasse invariant, the Igusa tower, etc. I will then explain how to construct Hida families of Drinfeld modular forms and also mention what can be done for finite slope forms. Time allowing, I'll mention a classicality result of the type « small slope implies classical ». Joint work with G. Rosso.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].