BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Geoff Vooys (Mount Allison University) DTSTART:20240326T150000Z DTEND:20240326T160000Z DTSTAMP:20260412T205031Z UID:voganish/8 DESCRIPTION:Title: Equivariant Beilinson's Theorem and Extensions of Equivariant Perverse Sh eaves\nby Geoff Vooys (Mount Allison University) as part of Canadian R ockies Representation Theory\n\nLecture held in Zoom and MS337.\n\nAbstrac t\nBeilinson's Theorem is an important theorem in algebraic geometry 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 variety $X$ over an algebraically closed field $K$ with $\\ell$ a positive integer pri me distinct from the characteristic of $K$. While a result of fundamental importance\, as it allows the computation of extensions between perverse s heaves in the derived category on $X$ to be performed in their own bounded derived category\, the equivariant version of this result has been elusiv e and known in general only for complex varieties with actions by finite c omplex algebraic groups. In this talk I'll discuss a general proof for an equivariant version of Beilinson's Theorem\, i.e.\,a triangulated equivale nce $D^b_G(X\;\\overline{\\mathbb{Q}}{\\ell}) \\simeq D^bG(\\mathbf{Perv} (X\;\\overline{\\mathbb{Q}}{\\ell}))$ which fixes the category of equivari ant perverse sheaves valid for any variety equipped with an action by a sm ooth algebraic group $G$ over a field $K$. Afterwards I'll give a short di scussion as well about what this means for equivariant extensions between equivariant perverse sheaves.\n\nI'll try to keep the category theory in t his talk to as gentle a level as possible and at as understandable a level as possible as well\, so please ask questions as we go!\n LOCATION:https://researchseminars.org/talk/voganish/8/ END:VEVENT END:VCALENDAR