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SUMMARY:Dualizing Complexes in the Noncommutative Arithmetic Context - R
 ishi Vyas (Ben-Gurion)
DTSTART:20170503T153000Z
DTEND:20170503T163000Z
UID:TALK72457@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:Dualizing complexes were first introduced in commutative alg
 ebra and\nalgebraic geometry by Grothendieck and play a fundamental role i
 n\nSerre-Grothendieck duality theory for schemes. The notion of\na dualiz
 ing complex was extended to noncommutative ring theory by Yekutieli.\nTh
 ere are existence theorems for dualizing complexes in the noncommutativ
 e\ncontext\, due to Van den Bergh\, Wu\, Zhang\, and Yekutieli amongst oth
 ers. \n\nMost considerations of dualizing complexes over noncommutativ
 e rings are for\nalgebras defined over fields. There are technical difficu
 lties involved in\nextending this theory to algebras defined over more gen
 eral commutative base\nrings. In this talk\, we will describe these challe
 nges and how to get around\nthem. Time permitting\, we will end by present
 ing an existence theorem\nfor dualizing complexes in this more general 
 setting. \n\nThe material described in this talk is work in progress\, ca
 rried out jointly\nwith Amnon Yekutieli. \n
LOCATION:MR12
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