Gelfand--Kirillov dimension and mod $p$ cohomology for quaternion algebras

Abstract: The Gelfand--Kirillov dimension is a classical invariant which measures the size of smooth representations of p-adic groups. It acquired particular relevance in the mod $p$ Langlands program because of work of Breuil--Herzig--Hu--Morra--Schraen, who computed it for the mod $p$ cohomology of $\mathrm{GL}_2$ over totally real fields, and used it to prove several structural properties of the cohomology. In this talk we will present a simplified proof of this result, which has the added benefit of working unchanged for nonsplit inner forms of $\mathrm{GL}_2$. This is joint work with Bao V. Le Hung.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html