On Emerton's $p$-adic Banach spaces

Details On Emerton's $p$-adic Banach spaces On Emerton's $p$-adic Banach spaces

2007-08-03

arxiv.org/abs/0708.0420v1

Mathematics

Number Theory

30 pages

Scientific paper

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.

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