Andrea Dotto

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

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 GL_2 over totally real fields, and used it to prove several structural properties of the cohomology. In this talk, after an overview, we will present a simplified proof of this result, which has the added benefit of working unchanged for nonsplit inner forms of GL_2. This is joint work with Bao V. Le Hung.