Rigid Dualizing Complexes on Schemes

Details Rigid Dualizing Complexes on Schemes Rigid Dualizing Complexes on Schemes

2004-05-29

arxiv.org/abs/math/0405570v3

Mathematics

Algebraic Geometry

60 pages, AMSLaTeX, xypic diagrams. Major changes: (1) added proof of residue theorem and duality for proper maps; (2) expande

Scientific paper

In this paper we present a new approach to Grothendieck duality on schemes. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. We obtain most of the important features of Grothendieck duality, yet manage to avoid lengthy and difficult compatibility verifications. Our results apply to finite type schemes over a regular noetherian finite dimensional base ring, and hence are suitable for arithmetic geometry.

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