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arXiv · 2402.17852

Descending finite projective modules from a Novikov ring

Dongryul Kim
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Abstract

We prove a descent result for finite projective modules, motivated by a question in perfectoid geometry. Given a commutative ring $A$, we formulate a descent problem for descending a finite projective module over the Novikov ring with coefficients in $A$ to a finite projective module over $A$. The main theorem of this paper is that all such descent data are effective. As an application, we prove for every perfect $\mathbb{F}_p$-algebra $A$, a vector bundle on $\operatorname{Spd} A$ always descends to a vector bundle on $\operatorname{Spec} A$.

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Dongryul Kim. 2024-02-27. Descending finite projective modules from a Novikov ring. https://arxiv.org/abs/2402.17852

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