Applications of duality theory to cousin complexes

Details Applications of duality theory to cousin complexes Applications of duality theory to cousin complexes

2005-12-05

arxiv.org/abs/math/0512105v3

Mathematics

Algebraic Geometry

40 pages. Substantially different from earlier version(s). To appear in Journal of Algebra

Scientific paper

We use the anti-equivalence between Cohen-Macaulay complexes and coherent sheaves on formal schemes to shed light on some older results and prove new results. We bring out the relations between a coherent sheaf M satisfying an S_2 condition and the lowest cohomology N of its "dual" complex. We show that if a scheme has a Gorenstein complex satisfying certain coherence conditions, then in a finite \'etale neighborhood of each point, it has a dualizing complex. If the scheme already has a dualizing complex, then we show that the Gorenstein complex must be a tensor product of a dualizing complex and a vector bundle of finite rank. We relate the various results in [S] on Cousin complexes to dual results on coherent sheaves on formal schemes.

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