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arXiv · 2501.13911

Algebraization of rigid analytic varieties and formal schemes via perfect complexes

Matteo Montagnani
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Abstract

In this paper, we extend a theorem of Toën and Vaquié 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.

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Matteo Montagnani. 2026-05-14. Algebraization of rigid analytic varieties and formal schemes via perfect complexes. https://arxiv.org/abs/2501.13911

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