论文标题
部分可观测时空混沌系统的无模型预测
Tensor weight structures and t-structures on derived categories of Noetherian schemes
论文作者
论文摘要
我们给出了一个特征的条件，该条件表征了来自基础方案的Thomason过滤的派生类别上的这些重量结构。满足我们病情的重量结构将称为$ \ otimes ^c $ - 加权结构。更确切地说，对于Noetherian分离的方案$ X $，我们在$ \ Mathbf {d}上的一组紧凑型生成的$ \ otimes ^C $ - 重量结构（\ Mathrm {qCoh \ hspace {1mm}}} X）$和$ x $的Thomason filtrations的集合。我们分为两个步骤实现此分类。首先，我们表明sťov\'ıček和posp \'ıšil限制的培训在一组紧凑的$ \ otimes ^c $ - 重量结构与紧凑型张量生成的Tensor t结构之间进行两次试验。然后，我们使用早期的紧凑量生成的T键T结构的分类来获得所需的结果。我们还研究了这些分类的一些直接后果，在投影线的特定情况下。我们表明，与Tensor t结构相比，$ \ Mathbf {d}^b（\ Mathrm {COH \ HSpace {1MM}}} \ Mathbb {p}^1_k）$。
We give a condition which characterises those weight structures on a derived category which come from a Thomason filtration on the underlying scheme. Weight structures satisfying our condition will be called $\otimes ^c$-weight structures. More precisely, for a Noetherian separated scheme $X$, we give a bijection between the set of compactly generated $\otimes ^c$-weight structures on $\mathbf{D} (\mathrm{Qcoh\hspace{1mm}}X)$ and the set of Thomason filtrations of $X$. We achieve this classification in two steps. First, we show that the bijection of Sťov\'ıček and Posp\'ıšil restricts to give a bijection between the set of compactly generated $\otimes ^c$-weight structures and the set of compactly generated tensor t-structures. We then use our earlier classification of compactly generated tensor t-structures to obtain the desired result. We also study some immediate consequences of these classifications in the particular case of the projective line. We show that in contrast to the case of tensor t-structures, there are no non-trivial tensor weight structures on $\mathbf{D}^b (\mathrm{Coh \hspace{1mm}} \mathbb{P}^1_k)$.
