Duality via cycle complexes

Thomas Geisser

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arXiv · math/0608456

Duality via cycle complexes

Thomas Geisser

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Abstract

We show that Bloch's complex of relative zero-cycles can be used as a dualizing complex over perfect fields and number rings. This leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields, finite fields, local fields of mixed characteristic, and rings of integers in number rings, generalizing results which so far have only been known for smooth schemes or in low dimensions, and unify the p-adic and l-adic theory. As an application, we generalize Rojtman's theorem to normal, projective schemes.

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BibTeX RIS

Thomas Geisser. 2008-11-26. Duality via cycle complexes. https://arxiv.org/abs/math/0608456

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