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SUMMARY:On the mod-p Cohomology of Certain p-saturable Groups
DTSTART:20260108T100000Z
DTEND:20260108T113000Z
DTSTAMP:20260504T073300Z
UID:indico-event-15736@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Konstantin Ardakov (Mathematical Institute\, Univers
 ity of Oxford)\n\nSéminaire de géométrie arithmétique\nThe mod-$p$ coh
 omology of equi-$p$-saturable pro-$p$ groups has been calculated by Lazard
  in the 1960s. Motivated by recent considerations in the mod-$p$ Langlands
  program\, we consider the problem of extending his results to the case of
  compact $p$-adic Lie groups $G$ that are $p$-saturable but not necessaril
 y equi-$p$-saturable: when $F$ is a finite extension of $\\mathbb{Q}_p$ an
 d $p$ is sufficiently large\, this class of groups includes the so-called 
 pro-$p$ Iwahori subgroups of $SL_n(F)$. In general\, using the work of Ser
 re and Lazard one can write down a spectral sequence that relates the mod-
 $p$ cohomology of $G$ to the cohomology of its associated graded mod-$p$ L
 ie algebra $\\mathfrak{g}$. We will discuss certain sufficient conditions 
 on $p$ and $G$ that ensure that this spectral sequence collapses. When the
 se conditions hold\, it follows that the mod-$p$ cohomology of $G$ is isom
 orphic to the cohomology of the Lie algebra $\\mathfrak{g}$.\n \n========
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LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/15736/
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