Faithfully flat descent of almost perfect complexes in rigid geometry

TL;DR

This paper proves a version of faithfully flat descent for almost perfect complexes in rigid analytic geometry, extending previous results on vector bundles without finiteness constraints.

Contribution

It introduces a generalized descent theorem for almost perfect complexes in rigid geometry, removing finiteness assumptions on rings.

Findings

Descent holds for almost perfect complexes in rigid analytic geometry.

Extends Drinfeld's results from vector bundles to complexes.

No finiteness assumptions required on the rings.

Abstract

We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results of Drinfeld for vector bundles.