Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Emerton's $p$-adic Banach spaces   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.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex