2012/11/17 by Odabaşı, Sinem
#13D30 #14F05 #18A30 #18E40 #18F20 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1211.4135
Let X be an arbitrary scheme. The category \mathfrakQcoh(X) of quasi--coherent sheaves on X is known that admits arbitrary direct products. However their structure seems to be rather mysterious. In the present paper we will describe the structure of the product object of a family of locally torsion-free objects in \mathfrakQcoh(X), for X an integral scheme. Several applications are provided. For instance it is shown that the class of flat quasi--coherent sheaves on a Dedekind scheme X is closed under arbitrary direct products, and that the class of all locally torsion-free quasi--coherent sheaves induces a hereditary torsion theory on \mathfrakQcoh(X). Finally torsion-free covers are shown to exist in \mathfrakQcoh(X).