GK-bound for p-adic Banach representations with infinitesimal character in families

Speaker: Reinier Sorgdrager ，Université Paris-Saclay 

Title: GK-bound for p-adic Banach representations with infinitesimal character in families

Language: English 

Time & Venue: 2026.05.08 10:00-12:00 MCM110

Abstract: Let p>2 and K be a p-adic field. I will briefly recall the key points of my work (arXiv:2602.08856) to bound from above by [K:Q_p] the Gelfand-Kirillov dimension of p-adic Banach representations of GL_2(K) with infinitesimal character. In work to appear I generalize this bound to p-adic Banach representations in families of GL_2(K) (or units of the quaternion algebra over K) with an infinitesimal character in families in the sense of Dospinescu-Paškūnas-Schraen. It allows one to bound the GK-dimension of mod p Hecke eigenspaces in the cohomology of Shimura varieties by [K:Q_p], as was done before by Breuil-Herzig-Hu-Morra-Schraen and Hu-Wang when K is unramified. In my talk I aim to explain the changes necessary to deal with families.