Serre injective sheaves
type: Item
instance of: scholarly article
title: Serre injective sheaves
zbMATH Open document ID: 0812.16007
DOI: 10.1007/BF01210434
author: A. B. Verevkin
published in: Mathematical Notes
publication date: 1994-04-12T00:00:00Z
review text: For \(k\) a field, \(V\) a finite dimensional vector space over \(k\) and \(T\) the tensor algebra of \(V\), the author studies a factor algebra, \(A\), of \(T\) modulo a one sided ideal. Considering \(\text{gr-}A\), the author factors by a full subcategory determined by colimits of certain bounded objects. The resulting factor category in the case that \(A\) is commutative, is equivalent to the category of quasi coherent sheaves on \(\text{Proj}(A)\) by results of Serre. The author calls this quotient category in the general case the category of Serre sheaves. (The translator uses `Serré' but this is clearly wrong.) The remainder of the paper explores cohomology in this category.
reviewed by: Timothy Porter
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 16D50
zbMATH DE Number: 525729
zbMATH Keywords: tensor algebra
zbMATH Keywords: factor category
zbMATH Keywords: category of quasi coherent sheaves
zbMATH Keywords: category of Serre sheaves
zbMATH Keywords: cohomology
Wikidata QID: Q114234010
MaRDI profile type: Publication
cites work: Faisceaux algébriques cohérents
cites work: Q5580926
description: scientific article; zbMATH DE number 525729