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SUMMARY:Cristian Popescu (UCSD)
DTSTART:20211104T233000Z
DTEND:20211105T010000Z
DTSTAMP:20260423T040542Z
UID:UCSBsga/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/29/"
 >An equivariant Tamagawa number formula for Drinfeld modules and beyond</a
 >\nby Cristian Popescu (UCSD) as part of UCSB Seminar on Geometry and Arit
 hmetic\n\n\nAbstract\nTo a Galois extension of characteristic p global fie
 lds and a suitable Drinfeld module\,\none can associate an equivariant\, c
 haracteristic p valued\, rigid analytic Goss-type L-function. \nI will dis
 cuss the construction of this L-function and the statement and proof of a 
 (Tamagawa number) formula for \nits special value at 0\,  which generalize
 s to the Galois equivariant setting Taelman's celebrated class-number form
 ula\, \nproved in 2012. Next\, I will show how this formula implies a perf
 ect analog of the Brumer-Stark conjecture for Drinfeld modules.\nIf time p
 ermits\, I will discuss the very recent extension of the above formula to 
 the much larger category of t-modules\n(t-motives)\, as well as its applic
 ations to the development of an Iwasawa theory for Drinfeld modules. The l
 ecture is based\non several recent joint works with N. Green\, J. Ferrara 
 and Z. Higgins.\n
LOCATION:https://researchseminars.org/talk/UCSBsga/29/
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