Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896474 | Journal of Algebra | 2018 | 13 Pages |
Abstract
Let Xâ¶fS be a morphism of Noetherian schemes, with S reduced. For any closed subscheme Z of X finite over S, let j denote the open immersion XâZâªX. Then for any coherent sheaf F on XâZ and any index râ¥1, the sheaf fâ(RrjâF) is generically free on S and commutes with base change. We prove this by proving a related statement about local cohomology: Let R be Noetherian algebra over a Noetherian domain A, and let IâR be an ideal such that R/I is finitely generated as an A-module. Let M be a finitely generated R-module. Then there exists a non-zero gâA such that the local cohomology modules HIr(M)âAAg are free over Ag and for any ring map AâL factoring through Ag, we have HIr(M)âALâ
HIâALr(MâAL) for all r.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Karen E. Smith,