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SUMMARY:Cristian Popescu (UC San Diego & IAS Princeton)
DTSTART:20260331T203000Z
DTEND:20260331T213000Z
DTSTAMP:20260423T130605Z
UID:MITNT/139
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/139/">
 An equivariant Tamagawa number formula for abelian $t$-motives and applica
 tions</a>\nby Cristian Popescu (UC San Diego & IAS Princeton) as part of M
 IT number theory seminar\n\nLecture held in Room 4-231 at MIT (Building 4)
 .\n\nAbstract\nWe will explain the construction of a Galois equivariant Go
 ss-type $L$-function associated to an abelian $t$-motive and outline the f
 ormulation and proof of a Tamagawa Number Formula for its special values a
 t positive integers. This generalizes to the abelian $t$-motive and equiva
 riant settings Taelman's celebrated class-number formula for Drinfeld modu
 les. If time permits\, we will show how the main result implies analogues 
 of the  Brumer-Stark and Coates-Sinnott Conjectures for abelian $t$-motive
 s. This is based on joint work with Ferrara\, Green\, Higgins and Ramachan
 dran.\n
LOCATION:https://researchseminars.org/talk/MITNT/139/
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