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Coherent functors. (English) Zbl 0921.13010

The purpose of the paper is to explain the general theory of coherent functors on the category of finitely generated modules over a noetherian ring \(A\), and to give some applications to cohomology of coherent sheaves on projective spaces. In the special case where \(A\) is a discrete valuation ring, a necessary and sufficient condition for a functor to be coherent is given in terms of commuting with certain inverse limits.
Several applications are given: Grothendieck’s relative duality theorem is stated in terms of dual coherent functors, the behavior under liaison of the Rao functor of a flat family of space curves is described, and a generalization of a theorem of Horrocks is given.

MSC:

13D99 Homological methods in commutative ring theory
18F05 Local categories and functors
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
14M06 Linkage
14H50 Plane and space curves
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