论文标题
T结构的HRS倾斜过程和胸部的心脏
The HRS tilting process and Grothendieck hearts of t-structures
论文作者
论文摘要
在本文中，我们回顾了确定T结构的核心何时是Grothendieck类别的问题，并特别注意了Happel-Reiten-Smalø（HSR）T结构在与Grothendieck类别类别的类别中相关的类别中与Torsion对的类别相关的类别。我们重新访问其HRS倾斜过程，从中得出许多有关HRS T结构的信息，这些HRS T结构具有投影生成器或注射式Cogenerator，并在成对$（\ Mathcal {A}，\ Mathbf {t}）中获得了几个BEXTIONS $。我们使用这些徒通过不同的方法，倾斜理论的最新结果以及以下事实重新启动，即如果$ \ m arthbf {t} =（\ Mathcal {t}，\ Mathcal {f}）$是在Grothendieck类别中的扭转对，则是grothendieck类别$ \ nathcal {g} $，然后是相关的heart heart hect other hect a groth he g s o hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs hs只有$ \ mathbf {t} $是有限类型的。我们调查了最后一个问题和解决方案后的最新结果。
In this paper we revisit the problem of determining when the heart of a t-structure is a Grothendieck category, with special attention to the case of the Happel-Reiten-Smalø (HSR) t-structure in the derived category of a Grothendieck category associated to a torsion pair in the latter. We revisit the HRS tilting process deriving from it a lot of information on the HRS t-structures which have a projective generator or an injective cogenerator, and obtain several bijections between classes of pairs $(\mathcal{A},\mathbf{t})$ consisting of an abelian category and a torsion pair in it. We use these bijections to re-prove, by different methods, a recent result of Tilting Theory and the fact that if $\mathbf{t}=(\mathcal{T},\mathcal{F})$ is a torsion pair in a Grothendieck category $\mathcal{G}$, then the heart of the associated HRS t-structure is itself a Grothendieck category if, and only if, $\mathbf{t}$ is of finite type. We survey this last problem and recent results after its solution.
