Faithfully flat descent of quasi-coherent complexes on rigid analytic varieties via condensed mathematics

TL;DR

This paper extends the concept of faithfully flat descent from pseudo-coherent complexes to quasi-coherent complexes on rigid analytic varieties using condensed mathematics, broadening the scope of descent theory in rigid geometry.

Contribution

It generalizes Mathew's faithfully flat descent result to quasi-coherent complexes on rigid analytic varieties through the framework of condensed mathematics.

Findings

Successfully extends descent results to a broader class of complexes.

Utilizes condensed mathematics to facilitate the generalization.

Provides a new foundation for descent in rigid analytic geometry.

Abstract

Faithfully flat descent of pseudo-coherent complexes in rigid geometry was proved by Mathew. In this paper, we generalize the result of Mathew to quasi-coherent complexes on rigid analytic varieties, which have been introduced by Clausen and Scholze by means of condensed mathematics.