Descent of restricted flat Mittag-Leffler modules and generalized vector bundles

Abstract

A basic question for any property of quasi--coherent sheaves on a scheme $X$ is whether the property is local, that is, it can be defined using any open affine covering of $X$. Locality follows from the descent of the corresponding module property: for (infinite dimensional) vector bundles and Drinfeld vector bundles, it was proved by Kaplansky's technique of dévissage already in \cite[II.\S3]{RG}. Since vector bundles coincide with ${\aleph }_0$-restricted Drinfeld vector bundles, a question arose in \cite{EGPT} of whether locality holds for $\kappa$-restricted Drinfeld vector bundles for each infinite cardinal $\kappa$. We give a positive answer here by replacing the d\' evissage with its recent refinement involving $\mathcal{C}$-filtrations and the Hill Lemma.

References in corpus (2)

• Almost free modules and Mittag--Leffler conditions
• Model category structures arising from Drinfeld vector bundles

Cited by in corpus (2)

• Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves
• Tate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)