Abstract
cf. [31, WI. In this paper we look at the problem in a different way. We want to consider torsion theories in the category of presheaves of modules over a fixed presheaf of rings. The functorial character of torsion theory, as set up by P. Gabriel, cf. [l], and 0. Goldman, cf. [4], invites direct generalization. On the other hand we also want earlier constructed structure (pre-) sheaves, cf. [3], [6], [7], to be the result of localization of a constant presheaf. Because of this we are forced to consider certain special torsion theories, called local torsion theories. These are locally defined by common kernel functors in module categories.
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