Almost Vector Bundles over Perfectoid Spaces

TL;DR

This paper introduces the concept of almost vector bundles over perfectoid spaces, proving a $v$-descent theorem and a structure theorem, advancing the understanding of vector bundles in the perfectoid setting.

Contribution

It defines almost vector bundles and proves foundational theorems, including $v$-descent and structure theorems, in the context of perfectoid spaces.

Findings

Established $v$-descent theorem for almost vector bundles

Proved a structure theorem for these bundles

Derived several intermediate results

Abstract

In this paper, we define vector bundles within the framework of almost mathematics (referred to as almost vector bundles) and establish the $v$-descent theorem together with a structure theorem for these bundles over perfectoid spaces. The proof yields several interesting intermediate results.