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arXiv · 1610.07715

A local duality principle in derived categories of commutative Noetherian rings

Tsutomu Nakamura·Yuji Yoshino
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Abstract

Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors with supports in arbitrary subsets of Spec R, which is a natural generalization of right derived functors of section functors with supports in specialization-closed subsets. We prove that the local duality theorem and the vanishing theorem of Grothendieck type hold for colocalization functors.

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Tsutomu Nakamura, Yuji Yoshino. 2016-10-25. A local duality principle in derived categories of commutative Noetherian rings. https://arxiv.org/abs/1610.07715

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