论文标题
诺瑟（Noetherian）戒指的心：扭转对和衍生的等价
Hearts for commutative noetherian rings: torsion pairs and derived equivalences
论文作者
论文摘要
通过$ \ MATHSF {mod}（r）$和$ \ Mathsf {d}（r）$的结构，通过支配支配，在交换noetherian环$ r $上，质谱控制。我们表明，就像在$ \ mathsf {mod}（r）$中一样，支持分配分类在任何不重新生成的$ \ mathsf {d}（r）$的非等级生成的$ t $结构的核心中。此外，我们调查了这些$ t $结构是否诱导派生的等价，获得了Grothendieck类别的新来源，该类别的派生等效于$ \ Mathsf {mod}（r）$。
Over a commutative noetherian ring $R$, the prime spectrum controls, via the assignment of support, the structure of both $\mathsf{Mod}(R)$ and $\mathsf{D}(R)$. We show that, just like in $\mathsf{Mod}(R)$, the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated $t$-structure of $\mathsf{D}(R)$. Moreover, we investigate whether these $t$-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to $\mathsf{Mod}(R)$.
