Constant families of t-structures on derived categories of coherent sheaves

dc.creatorPolishchuk, Alexander
dc.date2006-06-01
dc.date2006-12-20
dc.date.accessioned2026-07-07T07:36:18Z
dc.date.available2026-07-07T07:36:18Z
dc.descriptionWe 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.description26 pages, exposition improved, to appear in Moscow Math. Journal
dc.identifierhttps://arxiv.org/abs/math/0606013
dc.identifierhttp://arxiv.org/abs/math/0606013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120382
dc.subjectAlgebraic Geometry
dc.titleConstant families of t-structures on derived categories of coherent sheaves
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