A reinterpretation of Emerton's $p$-adic Banach spaces

TL;DR

This paper demonstrates that Emerton's $p$-adic Banach spaces are isomorphic to certain sheaf cohomology groups, providing new insights and applications in $p$-adic analysis.

Contribution

It establishes an isomorphism between Emerton's $p$-adic Banach spaces and sheaf cohomology groups, offering a reinterpretation of these spaces.

Findings

$p$-adic Banach spaces are isomorphic to sheaf cohomology groups

Provides new applications of the isomorphism in $p$-adic analysis

Enhances understanding of the structure of $p$-adic Banach spaces

Abstract

It is shown that the $p$-adic Banach spaces introduced by Emerton are isomorphic to the cohomology groups of the sheaf of continuous $\Q_{p}$-valued functions on a certain space. Some applications of this result are discussed.