An equivariant Tamagawa number formula for abelian $t$-motives and applications

Abstract: We will explain the construction of a Galois equivariant Goss-type $L$-function associated to an abelian $t$-motive and outline the formulation and proof of a Tamagawa Number Formula for its special values at positive integers. This generalizes to the abelian $t$-motive and equivariant settings Taelman's celebrated class-number formula for Drinfeld modules. If time permits, we will show how the main result implies analogues of the Brumer-Stark and Coates-Sinnott Conjectures for abelian $t$-motives. This is based on joint work with Ferrara, Green, Higgins and Ramachandran.

algebraic geometrynumber theory

Audience: researchers in the topic

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MIT number theory seminar

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