Abstract:We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category $\mathrm {D}({\mathrm {Mod}}\text {-}A)$ of a ring $A$. To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in $A$, which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in $\mathrm {D}({\mathrm {Mod}}\text {-}A)$. This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.

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中文翻译：

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在派生类别中参数化扭转对

摘要：我们在无界派生类别 $\mathrm {D}({\mathrm {Mod}}\text {-}A) $ 一个戒指 $A$。为此，我们提供了从 $A$ 开始的环同态晶格中的链的 t 结构构造，这是从 Zariski 谱的子集链构造紧凑生成的 t 结构的自然扩展可交换的诺特案例。我们还在 $\mathrm {D}({\mathrm {Mod}}\text {-}A)$ 中提供了淤泥和共淤对象的构造。这导致我们对某些类型的交换环和有限维遗传代数的分类结果。

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