Duality and flat base change on formal schemes
摘要
We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's method for the special case of ordinary schemes, are reasonably self-contained, modulo the Special Adjoint Functor Theorem. An alternative approach, inspired by Neeman and based on recent results about "Brown Representability," is indicated as well. A section on applications and examples illustrates how these theorems synthesize a number of different duality-related results (local duality, formal duality, residue theorems, dualizing complexes...). A flat-base-change theorem for pseudo-proper maps leads in particular to sheafified versions of duality for bounded-below complexes with quasi-coherent homology. Thanks to Greenlees-May duality, the results take a specially nice form for proper maps and bounded-below complexes with coherent homology.
引用
@article{arxiv.alg-geom/9708006,
title = {Duality and flat base change on formal schemes},
author = {Leovigildo Alonso and Ana Jeremias and Joseph Lipman},
journal= {arXiv preprint arXiv:alg-geom/9708006},
year = {2008}
}
备注
89 pages. Change from published version: in section 2.5, about dualizing complexes on formal schemes, a weakening of one flawed Lemma is proved, and shown adequate for the several applications made of the original. For another correction, see math.AG/0106239