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SUMMARY:Federico Scavia (University of British Columbia)
DTSTART:20201022T210000Z
DTEND:20201022T220000Z
DTSTAMP:20260423T024743Z
UID:JNTS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/3/">Mot
 ivic classes of classifying stacks of algebraic groups</a>\nby Federico Sc
 avia (University of British Columbia) as part of Columbia CUNY NYU number 
 theory seminar\n\n\nAbstract\nThe Grothendieck ring of algebraic stacks wa
 s introduced by Ekedahl in \n2009. It may be viewed as a localization of t
 he more classical Grothendieck \nring of varieties. If $G$ is a finite gro
 up\, then the class\n $\\{BG\\}$ of its \nclassifying stack $BG$ is equal 
 to 1 in many cases\, but there are examples \nfor which $\\{BG\\}\\neq 1.$
   When $G$ is connected\, $\\{BG\\}$  has been computed in many \ncases in
  a long series of papers\, and it always turned out that $\\{BG\\}*\\{G\\}
 =1.$ \nWe exhibit the first example of a connected group $G$ for which $\\
 {BG\\}*\\{G\\}\\neq \n1.$  As a consequence\, we produce an infinite famil
 y of non-constant finite \n\\'etale group schemes $A$ such that $\\{BA\\}\
 \neq 1.$\n
LOCATION:https://researchseminars.org/talk/JNTS/3/
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