Duality and flat base change on formal schemes
| dc.creator | Alonso, Leovigildo | |
| dc.creator | Jeremias, Ana | |
| dc.creator | Lipman, Joseph | |
| dc.date | 1997-08-04 | |
| dc.date | 2005-11-19 | |
| dc.date.accessioned | 2026-07-07T09:01:54Z | |
| dc.date.available | 2026-07-07T09:01:54Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9708006 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9708006 | |
| dc.identifier | Contemporary Math. 244 (1999), 3-90 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148441 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14Fxx | |
| dc.title | Duality and flat base change on formal schemes | |
| dc.type | text |