On the mod-p cohomology of certain p-saturable groups.

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• Konstantin Ardakov, University of Oxford
• Wednesday 20 November 2024, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Adam Jones.

The mod-p cohomology of uniform 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 necessarily uniform pro-p: when F is a finite extension of Q_p and p is sufficiently large, this class of groups includes the so-called pro-p Iwahori subgroups 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 its associated graded mod-p Lie algebra $g$. We will discuss certain sufficient conditions on p and G that ensure that this spectral sequence collapses. When these conditions hold, it follows that the mod-p cohomology of G is isomorphic to the cohomology of the Lie algebra $g$.

This talk is part of the Algebra and Representation Theory Seminar series.

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