2011/10/24 by Sergio Estrada, Estrada, Sergio, Pedro A. Guil Asensio +3
Mathematics · #03E35 (Secondary) 13D07 #14F05 (Primary) 16D40 #18E15 #55N30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1110.5364
openalex publication_date 2011/10/24 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
A basic question for any property of quasi--coherent sheaves on a scheme X\nis whether the property is local, that is, it can be defined using any open\naffine covering of X. Locality follows from the descent of the corresponding\nmodule property: for (infinite dimensional) vector bundles and Drinfeld vector\nbundles, it was proved by Kaplansky's technique of d 'evissage already in\n cite[II. S3]RG. Since vector bundles coincide with \ℵ0-restricted\nDrinfeld vector bundles, a question arose in citeEGPT of whether locality\nholds for \κ-restricted Drinfeld vector bundles for each infinite\ncardinal \κ. We give a positive answer here by replacing the d ' evissage\nwith its recent refinement involving mathcal C-filtrations and the Hill\nLemma.\n