论文标题
用于遗传类别的衍生类别的淤积物体的减少方法
A reduction approach to silting objects for derived categories of hereditary categories
论文作者
论文摘要
令$ \ Mathcal {h} $为具有有限尺寸$ \ perperatorname {hom} $和$ \ operatorname {ext} $ space的字段$ k $的遗传性阿贝利安类别。事实证明，有限的派生类别$ \ MATHCAL {d}^b（\ MATHCAL {h}）$具有一个灰烬对象，如果F $ \ MATHCAL {H} $具有倾斜对象Iff $ \ Mathcal {d}^b（d}^b（d}^b（\ nathcal {h}）$ ext $ ext $ ext $ ext $ ext $ acivir $ act ac ac acy cartearn $ - 一路上，我们获得了一个新的证明，证明了$ \ Mathcal {d}^b（\ Mathcal {h}）$的每个主持对象都是部分淤积对象。我们还考虑了对简单有思想的收藏的补充问题。与推荐对象相反，$ \ Mathcal {r} $ of $ \ MATHCAL {d}^b（\ Mathcal {h}）$的$ \ Mathcal {r} $可以完成简单的集合，即$ \ operatatorNorname {ext} $ - $ \ nathcal的Quiviver $ \ Mathcal {R} $ acyc LIC {R} $ acyclic is Acyc acy acy。
Let $\mathcal{H}$ be a hereditary abelian category over a field $k$ with finite dimensional $\operatorname{Hom}$ and $\operatorname{Ext}$ spaces. It is proved that the bounded derived category $\mathcal{D}^b(\mathcal{H})$ has a silting object iff $\mathcal{H}$ has a tilting object iff $\mathcal{D}^b(\mathcal{H})$ has a simple-minded collection with acyclic $\operatorname{Ext}$-quiver. Along the way, we obtain a new proof for the fact that every presilting object of $\mathcal{D}^b(\mathcal{H})$ is a partial silting object. We also consider the question of complements for pre-simple-minded collections. In contrast to presilting objects, a pre-simple-minded collection $\mathcal{R}$ of $\mathcal{D}^b(\mathcal{H})$ can be completed into a simple-minded collection iff the $\operatorname{Ext}$-quiver of $\mathcal{R}$ is acyclic.
