Rigid dualizing complexes on schemes Academic Article uri icon

abstract

  • Warning: this preprint is sketchy and the proofs in it are far from complete. Please look up the survey article and the lecture notes. Full proofs should appear during 2015. ------------------------------------ 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.

publication date

  • January 1, 2004

published in