Algebraization of rigid analytic varieties and formal schemes via perfect complexes
Algebraic Geometry
2026-05-15 v3
Abstract
In this paper, we extend a theorem of To\"en and Vaqui\'e to the non-Archimedean and formal settings. More precisely, we prove that a smooth and proper rigid analytic variety is algebraizable if and only if its category of perfect complexes is smooth and proper. As a corollary, we deduce an analogous statement for formal schemes and demonstrate that, in general, the bounded derived category of coherent sheaves on a formal scheme is not smooth.
Cite
@article{arxiv.2501.13911,
title = {Algebraization of rigid analytic varieties and formal schemes via perfect complexes},
author = {Matteo Montagnani},
journal= {arXiv preprint arXiv:2501.13911},
year = {2026}
}
Comments
Text significantly revised for better clarity; main results unchanged