Applications of duality theory to cousin complexes

Suresh Nayak; Pramathanath Sastry

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Applications of duality theory to cousin complexes

Suresh Nayak·Pramathanath Sastry

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Abstract

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 étale 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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BibTeX RIS

Suresh Nayak, Pramathanath Sastry. 2007-07-10. Applications of duality theory to cousin complexes. https://arxiv.org/abs/math/0512105

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