Constant families of t-structures on derived categories of coherent sheaves
Constant families of t-structures on derived categories of coherent sheaves
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相干滑轮派生类别上的 T 结构常数族
DOI：
10.17323/1609-4514-2007-7-1-109-134
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发表时间：
2006
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影响因子：
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通讯作者：
A. Polishchuk
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文献类型：
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作者：
A. Polishchuk
我们推广数学中给出的构造。AG/0309435的“常数”t型结构在相干轴的有界派生范畴$D(X\times S)$上，从$D(X)$上的t型结构开始。也就是说，我们去除$X$和$S$上的平滑性和拟投射性假设，并使用不一定是诺etherian但在适当意义上接近诺etherian的t结构。主要的新工具是构造诱导t结构，它使用无界派生类的准相干轴，并依赖于\cite{AJS}的结果。作为“常数”t结构技术的一个应用，我们证明了$D(X)$上每一个具有Noetherian心的有界非退化t结构在$D(X)$的一组连通的自等价作用下是不变的。此外，我们还证明了如果$X$是光滑的，那么$D(X)$上唯一的局部t结构，即对于所有开放的$U\subset X$，在$D(U)$上存在兼容t结构的那些，是在math.AG/0005152中考虑的反常t结构。
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.