Drinfeld's Elliptic Sheaves and Generalizations

Abstract: In this talk, we will explore the area of function field arithmetic, with a focus on Drinfeld's elliptic sheaves and their generalizations, as well as analogies to the number field setting. Drinfeld modules, introduced in 1974 as analogues of elliptic curves in the function field setting, play a central role in this context. To establish a Langlands correspondence, Drinfeld studied moduli spaces of elliptic sheaves, or equivalently, shtukas. After a brief introduction to the function field framework, we will examine some well-known generalizations of elliptic sheaves, concentrating on generalized D-elliptic sheaves and presenting results on their moduli spaces. In the final part of the talk, we will explore the connections between (generalized) shtukas and (generalized) elliptic sheaves.

algebraic geometrynumber theory

Audience: researchers in the topic

FGC-HRI-IPM Number Theory Webinars

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