Duality via cycle complexes

Details Duality via cycle complexes Duality via cycle complexes

2006-08-18

arxiv.org/abs/math/0608456v3

Mathematics

Algebraic Geometry

Updated and improved version; accepted at Annals of Mathematics

Scientific paper

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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