Duality via cycle complexes

• 成果类型: Article
• 署名作者: Geisser, Thomas
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1095-1126
• 关键词: artin-verdier duality; torsion zero-cycles; K-THEORY; MOTIVIC COHOMOLOGY; algebraic cycles; VARIETIES; THEOREM; FIELDS; conjecture

摘要

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 unifying the p-adic and l-adic theory. As an application, we generalize Rojtman's theorem to normal, projective schemes.