BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:John Greenlees (University of Warwick) DTSTART:20210916T060000Z DTEND:20210916T073000Z DTSTAMP:20260412T203539Z UID:SAGO/10 DESCRIPTION:Title: Th e singularity category of C^*(BG) for a finite group G\nby John Greenl ees (University of Warwick) as part of Algebra Seminar (presented by SMRI) \n\n\nAbstract\nAbstract: The cohomology ring H^*(BG) (with coefficients i n a field k of characteristic p) is a very special graded commutative ring \, but this comes out much more clearly if one uses the cochains C^*(BG)\ , which can be viewed as a commutative ring up to homotopy. For example C ^*(BG) is always Gorenstein (whilst this is not quite true for H^*(BG)). \ n\nThis leads one to study C^*(BG) as if it was a commutative local Noethe rian ring\, though of course one has to use homotopy invariant methods. Th e ring C^*(BG) is regular if and only if G is p-nilpotent and so it is nat ural to look for ways of deciding where C^*(BG) lies on the spectrum betwe en regular and Gorenstein rings. For a commutative Noetherian ring\, one c onsiders the singularity category D_{sg}(R) (the quotient of finite comple xes of finitely generated modules by finitely generated projectives). This is trivial if and only if R is regular\, so is the appropriate tool. The talk will describe how to define this for C^*(BG)\, show it has good basic properties and describe the singularity category in the simplest case it is not trivial (when G has a cyclic Sylow p-subgroup).\n LOCATION:https://researchseminars.org/talk/SAGO/10/ END:VEVENT END:VCALENDAR