Constant families of t-structures on derived categories of coherent sheaves
| dc.creator | Polishchuk, Alexander | |
| dc.date | 2006-06-01 | |
| dc.date | 2006-12-20 | |
| dc.date.accessioned | 2026-07-07T07:36:18Z | |
| dc.date.available | 2026-07-07T07:36:18Z | |
| dc.description | We generalize the construction given in math.AG/0309435 of a "constant" t-structure on the bounded derived category of coherent sheaves $D(X\times S)$ starting with a t-structure on $D(X)$. Namely, we remove smoothness and quasiprojectivity assumptions on $X$ and $S$ and work with t-structures that are not necessarily Noetherian but are close to Noetherian in the appropriate sense. The main new tool is the construction of induced t-structures that uses unbounded derived categories of quasicoherent sheaves and relies on the results of \cite{AJS}. As an application of the "constant" t-structures techniques we prove that every bounded nondegenerate t-structure on $D(X)$ with Noetherian heart is invariant under the action of a connected group of autoequivalences of $D(X)$. Also, we show that if $X$ is smooth then the only local t-structures on $D(X)$, i.e., those for which there exist compatible t-structures on $D(U)$ for all open $U\subset X$, are the perverse t-structures considered in math.AG/0005152. | |
| dc.description | 26 pages, exposition improved, to appear in Moscow Math. Journal | |
| dc.identifier | https://arxiv.org/abs/math/0606013 | |
| dc.identifier | http://arxiv.org/abs/math/0606013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120382 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Constant families of t-structures on derived categories of coherent sheaves | |
| dc.type | text |