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SUMMARY:Dustin Clausen (Bonn/Copenhagen)
DTSTART:20200601T150000Z
DTEND:20200601T170000Z
DTSTAMP:20260423T021438Z
UID:eAKTS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/eAKTS/1/">Th
 e K-theory of adic spaces</a>\nby Dustin Clausen (Bonn/Copenhagen) as part
  of electronic Algebraic K-theory Seminar\n\n\nAbstract\nMorrow and Kerz-S
 aito-Tamme have each proposed a definition\nfor the K-theory of rigid anal
 ytic varieties.  They start with a\nconstruction on affinoids\, then use p
 ro-cdh descent of usual algebraic\nK-theory (a theorem of Kerz-Strunk-Tamm
 e) to see that their\nconstruction satisfies descent for rigid coverings\,
  which lets one\nextend it to the global case.  We propose a definition wh
 ich is\ninherently global in nature\, and for which descent can be proven 
 in a\nsimilar manner to the Zariski descent of usual algebraic K-theory.  
 We\nrely on the theory of "solid modules"\, a convenient replacement for\n
 the usual notion of linearly topologized modules\, plus Efimov's\nbeautifu
 l observation that K-theory naturally makes sense for certain\nlarge (dual
 izable presentable) categories.  Namely\, we take the Efimov\nK-theory of 
 a full subcategory of solid modules called "nuclear".\nThis is joint work 
 with Peter Scholze.\n
LOCATION:https://researchseminars.org/talk/eAKTS/1/
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