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SUMMARY:Semistability of G-torsors and parabolic subgroups in positive cha
 racteristic
DTSTART:20230606T141500
DTEND:20230606T160000
DTSTAMP:20260427T224616Z
UID:fc2b26bb61997f6b372e148e5c825c6f6d9ecdb409597fb110c41743
CATEGORIES:Conferences - Seminars
DESCRIPTION:Marion Jeannin (Université d'Uppsala)\nLet k be a field and X
  be a k-curve. Let also G be a reductive group scheme over X. Semistabilit
 y for G-torsors can be defined by several ways that depend on assumptions 
 on k and G. These approaches are both well defined and equivalent when k i
 s of characteristic zero. In this talk I will explain in which generalitie
 s it is possible to extend some of these approaches to the positive charac
 teristic framework and compare them. This requires to investigate whether 
 some well known results in representation theory in characteristic zero st
 ill hold true in characteristic p > 0. More specifically\, an analogous st
 atement of a theorem of Morozov (which classifies\, in characteristic 0\, 
 parabolic subalgebras of the Lie algebra of a reductive group by means of 
 their nilradical) is a cornerstone of all this unification attempt.\n\n\nI
 n the first part of the talk\, I will provide an overview of the geometric
  content and emphasize\nthe role of parabolic subgroups in all this theory
  of semistability. The second part of the talk\nwill be dedicated to the e
 xtension of Morozov’s theorem to positive characteristics\, and the way 
 it allows one to get a more uniform vision of the different historical def
 initions of semistability of G-torsors.
LOCATION:GR A3 31 https://plan.epfl.ch/?room==GR%20A3%2031
STATUS:CONFIRMED
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