逗号范畴中的倾斜对象与挠对

Torsion classes generated by silting modules

We study the classes of modules which are generated by a silting module. In the case of either hereditary or perfect rings it is proved that these are exactly the torsion $\mathcal{T}$ such that the regular module has a special $\mathcal{T}$-preenvelope. In particular every torsion enveloping class in $\textrm{Mod-} R$ are of the form $\mathrm{Gen}(T)$ for a minimal silting module $T$. For the dual case we obtain for general rings that the covering torsion-free classes of modules are exactly the classes of the form $\mathrm{Cogen}(T)$, where $T$ is a cosilting module.

与扩展心相关的沉默子范畴和(余)挠对

Silting subcategories and (co)torsion pairs associated to extended hearts

建立了(d+1)-项沉默子范畴、d-扩展心中的函子有限s-挠对以及适当子范畴中的遗传完全余挠对之间的偏序集同构，并给出了dg代数版本。

On the abundance of silting modules

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or of a finite dimensional algebra of finite representation type, can be parametrised by silting modules. In these notes, we give a brief introduction to the fairly recent concepts of silting and cosilting module, and we explain the classification results mentioned above.

Silting objects

We give an overview of recent developments in silting theory. After an introduction on torsion pairs in triangulated categories, we discuss and compare different notions of silting and explain the interplay with t-structures and co-t-structures. We then focus on silting and cosilting objects in a triangulated category with coproducts and study the case of the unbounded derived category of a ring. We close the survey with some classification results over commutative noetherian rings and silting-discrete algebras.

极限与余极限在丝定理论中的应用及在代数墙和房间结构中的应用

Limits and colimits in silting theory with applications to the wall and chamber structure of an algebra

本文研究了由丝定对象定义的嵌套t-结构，并构造了对应于这些t-结构的aisles交集的丝定对象作为同调余极限。结果应用于构造两类大型丝定对象，对应于数值 torsion 对和墙和房间结构中的极限墙。

Silting modules

We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $τ$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten. We show that silting modules generate torsion classes that provide left approximations, and that every partial silting module admits an analogue of the Bongartz complement. Furthermore, we prove that silting modules are in bijection with 2-term silting complexes and with certain t-structures and co-t-structures in the derived module category. We also see how som…