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Statut |
Confirmé |
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Série |
MATH-IHES |
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Domaines |
math |
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Date |
Jeudi 8 Janvier 2026 |
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Heure |
11:00 |
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Institut |
IHES |
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Salle |
Amphithéâtre Léon Motchane |
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Nom de l'orateur |
Ardakov |
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Prenom de l'orateur |
Konstantin |
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Addresse email de l'orateur |
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Institution de l'orateur |
Mathematical Institute, University of Oxford |
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Titre |
On the mod-p Cohomology of Certain p-saturable Groups |
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Résumé |
The mod-$p$ cohomology 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 necessarily equi-$p$-saturable: when $F$ is a finite extension of $\mathbb{Q}_p$ and $p$ is sufficiently large, this class of groups includes the so-called pro-$p$ Iwahori subgroups of $SL_n(F)$. In general, using the work of Serre 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-$p$ Lie algebra $\mathfrak{g}$. 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 $\mathfrak{g}$. |
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Numéro de preprint arXiv |
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Commentaires |
Séminaire de Géométrie Arithmétique |
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Fichiers attachés |
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