Sheaves of t-structures and valuative criteria for stable complexes
| dc.creator | Abramovich, Dan | |
| dc.creator | Polishchuk, Alexander | |
| dc.date | 2003-09-26 | |
| dc.date | 2006-02-05 | |
| dc.date.accessioned | 2026-07-07T06:35:44Z | |
| dc.date.available | 2026-07-07T06:35:44Z | |
| dc.description | In this work more questions arise than answers given, for which of course we do not apologize. The core of this paper is concerned with the construction of a ``constant'' t-structure on the bounded derived category of coherent sheaves $D(X\times S)$, with $X$ and $S$ smooth varieties, given a nondegenerate t-structure on $D(X)$ with noetherian heart. While we believe this construction and the methods involved should be generally useful in studying derived categories, we present here but one application: we prove a valuative criterion for separation and properness for the collection P(1) of stable objects of phase 1 under a numerical, locally finite and noetherian Bridgeland-Douglas stability condition $(Z,\cP)$ on $D(X)$, where $X$ is a smooth projective variety. As an immediate result, the number of long-exact sequences in the first named author's output is no longer an embarrassment. | |
| dc.description | 33 pages. To appear in Crelle's Journal. This version incorporates an erratum in section 2.4 | |
| dc.identifier | https://arxiv.org/abs/math/0309435 | |
| dc.identifier | http://arxiv.org/abs/math/0309435 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99880 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 18E30; 14D20; 14F05 | |
| dc.title | Sheaves of t-structures and valuative criteria for stable complexes | |
| dc.type | text |