BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mikala Jansen (Copenhagen) DTSTART:20201027T160000Z DTEND:20201027T170000Z DTSTAMP:20260423T053046Z UID:eAKTS/15 DESCRIPTION:Title: T he reductive Borel--Serre compactification as a model for the K-theory spa ce\nby Mikala Jansen (Copenhagen) as part of electronic Algebraic K-th eory Seminar\n\nLecture held in 915 7106 9041.\n\nAbstract\nThe reductive Borel--Serre compactification\, introduced by Zucker in 1982\, is a strati fied space which is well suited for the study of $L^2$-cohomology of arith metic groups and has come to play a central role in the theory of compacti fications. We determine its stratified homotopy type (the exit path $\\inf ty$-category) to be a $1$-category defined purely in terms of parabolic su bgroups. This category makes sense in a much more general setting\, in fac t for any exact category\, but in this talk we restrict ourselves to well- behaved rings. With direct sum\, these naturally give rise to a monoidal c ategory\, and we show that (the loop space of the classifying space of) th is monoidal category is a model for the K-theory space. For finite fields\ , we encounter much better homological stability properties than for the g eneral linear groups.\n LOCATION:https://researchseminars.org/talk/eAKTS/15/ END:VEVENT END:VCALENDAR