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SUMMARY:Arithmetic of Bruhat-Tits group schemes over semilocal dedekind ri
 ngs
DTSTART:20261001T120000Z
DTEND:20261001T170000Z
DTSTAMP:20260928T110500Z
UID:indico-event-17113@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anis Zidani\n\nLet R be a DVR and G a reductive grou
 p over K = Frac(R). We say P is a Bruhat-Tits group scheme over R if\, for
  every maximal ideal m of R\, P is Bruhat-Tits (in the usual sense) over t
 he completion of R at m.In our setting\, a Bruhat-Tits group scheme over a
  complete DVR can be a parahoric group scheme\, the stabilizer of a point\
 , or even the lft Néron model of a torus\, or even more exotic group sche
 mes.\nThe key question of the talk is to understand when the map H^1(R\,P)
  --> H^1(K\,G) is injective.This question was originally posed by Bayer an
 d First in their study of classical groups and hereditary orders.The Groth
 endieck-Serre conjecture over R (proved by Nisnevich and Guo) is the speci
 al case where P is reductive over R.\nWe first lay the groundwork for stud
 ying the question\, then show that the map is always injective when G is s
 emisimple simply connected (for any P).We also give some counterexamples w
 here injectivity fails.We also give a simplified proof of the Grothendieck
 -Serre conjecture over R\, a proof that fits more within a building approa
 ch.\n\nhttps://indico.math.cnrs.fr/event/17113/
LOCATION:M7-411 (UMPA)
URL:https://indico.math.cnrs.fr/event/17113/
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