On Emerton's $p$-adic Banach spaces

Abstract

The purpose of the current paper is to introduce some new methods for studying the $p$-adic Banach spaces introduced by Emerton \cite{emerton}. We first relate these spaces to more familiar sheaf cohomology groups. As an application, we obtain a more general version of Emerton's spectral sequence. We also calculate the spaces in some easy cases. As a consequence, we obtain a number of vanishing theorems.

30 pages

References in corpus (3)

• Locally analytic vectors in representations of locally p-adic analytic groups
• Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups
• Bounds for Multiplicities of Unitary Representations of Cohomological Type in Spaces of Cusp Forms