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SUMMARY:Geoff Vooys - Deferred (Mount Allison University)
DTSTART:20240319T150000Z
DTEND:20240319T160000Z
DTSTAMP:20260412T205248Z
UID:voganish/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/voganish/6/"
 >Equivariant Beilinson's Theorem and Extensions of Equivariant Perverse Sh
 eaves</a>\nby Geoff Vooys - Deferred (Mount Allison University) as part of
  Canadian Rockies Representation Theory\n\nLecture held in Zoom and MS337.
 \n\nAbstract\nBeilinson's Theorem is an important theorem in algebraic geo
 metry that says there is a triangulated equivalence of categories $D^bc(X\
 ;\\overline{\\mathbb{Q}}{\\ell}) \\simeq D^b(\\mathbf{Perv}(X\;\\overline{
 \\mathbb{\\Q}}{\\ell}))$ fixing the category of perverse sheaves for any v
 ariety $X$ over an algebraically closed field $K$ with $\\ell$ a positive 
 integer prime distinct from the characteristic of $K$. While a result of f
 undamental importance\, as it allows the computation of extensions between
  perverse sheaves in the derived category on $X$ to be performed in their 
 own bounded derived category\, the equivariant version of this result has 
 been elusive and known in general only for complex varieties with actions 
 by finite complex algebraic groups. In this talk I'll discuss a general pr
 oof for an equivariant version of Beilinson's Theorem\, i.e.\,a triangulat
 ed equivalence  $D^b_G(X\;\\overline{\\mathbb{Q}}{\\ell}) \\simeq D^bG(\\m
 athbf{Perv}(X\;\\overline{\\mathbb{Q}}{\\ell}))$ which fixes the category 
 of equivariant perverse sheaves valid for any variety equipped with an act
 ion by a smooth algebraic group $G$ over a field $K$. Afterwards I'll give
  a short discussion as well about what this means for equivariant extensio
 ns between equivariant perverse sheaves.\n
LOCATION:https://researchseminars.org/talk/voganish/6/
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