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SUMMARY:On the mod-p cohomology of certain p-saturable groups. - Konstanti
 n Ardakov\, University of Oxford
DTSTART:20241120T163000Z
DTEND:20241120T173000Z
UID:TALK222817@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:The mod-p cohomology of uniform pro-p groups has been calculat
 ed by Lazard in the 1960s. Motivated by recent considerations in the mod-p
  Langlands program\, we consider the problem of extending his results to t
 he case of compact p-adic Lie groups G that are p-saturable but not necess
 arily uniform pro-p: when F is a finite extension of Q_p and p is sufficie
 ntly large\, this class of groups includes the so-called pro-p Iwahori sub
 groups of SL_n(F). In general\, there is a spectral sequence due to Serre 
 and Lazard that relates the mod-p cohomology of $G$ to the cohomology of i
 ts associated graded mod-p Lie algebra $g$. We will discuss certain suffic
 ient conditions on p and G that ensure that this spectral sequence collaps
 es. When these conditions hold\, it follows that the mod-p cohomology of G
  is isomorphic to the cohomology of the Lie algebra $g$.
LOCATION:MR12
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