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SUMMARY:Hyperbolic Localization and Second Adjointness [MPIM]
DTSTART:20250711T120500Z
DTEND:20250711T140000Z
DTSTAMP:20260415T104600Z
UID:indico-event-548@math-events.uni-bonn.de
DESCRIPTION:Speakers: Lucas Mann (Universität Münster)\n\nOberseminar Ar
 ithmetic Geometry and Representation Theory\nFollowing an idea of Drinfeld
 \, we present an abstract proof of Braden's\nresult on hyperbolic localiza
 tion\, relating sheaves on a space with\n$\\mathbb G_m$-action to their re
 striction to the attractor\, repeller and\nfixed point locus. Our argument
  is purely formal and works in an\nabstract setting\, and it roughly reduc
 es the general statement to the\nbase case of $\\mathbb G_m$ acting on $\\
 mathbb A^1$.  This allows us to\nextend the result to stacks and to arbitr
 ary 6-functor formalisms.\nApplying the result to the classifying stack of
  a reductive group\, we\nobtain new results on second adjointness for smoo
 th representations in\nnatural characteristic\, and we expect a similar ve
 rsion for locally\nanalytic representations as well as other applications 
 to various\ngeometric incarnations of second adjointness in the Langlands 
 program.\nThe main technical difficulty lies in handling the higher catego
 ry\ntheory involved in the argument\, and we have found efficient ways to\
 ndeal with "enriched (infty\,2)-categories" and lax functors between them.
 \nThis is joint work with Claudius Heyer.\n\nhttps://math-events.uni-bonn.
 de/event/548/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/548/
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