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.
arXiv Mathematics e-prints
- Pub Date:
- May 2004
- Mathematics - Algebraic Geometry;
- Primary: 14F05;
- Secondary: 14B25;
- This preprint is withdrawn because it is sketchy, and the proofs in it are far from complete. The authors are presently working on an improved version of this material (both correct and enhanced). Until then the interested reader can look up: (1) Section 13.5 of the book "Derived Catgeories", Cambridge U. Press 2019, prepublication version arXiv:1610.09640v4. (2) The lecture notes "Residues and Duality for Schemes and Stacks" at https://www.math.bgu.ac.il/~amyekut/lectures/resid-stacks/abstract.html