Abstract:Let $\mathscr {T}$ be a well generated triangulated category, and let $S\subset \mathscr {T}$ be a set of objects. We prove that there is a $t$-structure on $\mathscr {T}$ with $\mathscr {T}^{\leq 0}=\overline {\langle S \rangle }^{(-\infty ,0]}$. This article is an improvement on the main result of Alonso, Jeremías and Souto [Trans. Amer. Soc. 355 (2003), pp. 2523–2543], in which the theorem was proved under the assumption that $\mathscr {T}$ has a nice enough model. It should be mentioned that the result in Alonso, Jeremías and Souto has been influential—it turns out to be interesting to study all of these $t$-structures.

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中文翻译：

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由对象生成的𝑡结构

摘要：令$\mathscr {T}$ 为生成良好的三角范畴，并令$S\subset \mathscr {T}$ 为一组对象。我们证明 $\mathscr {T}$ 上存在 $t$-结构，其中 $\mathscr {T}^{\leq 0}=\overline {\langle S \rangle }^{(-\infty ,0 ]}$. 本文是对 Alonso、Jeremías 和 Souto [Trans. Amer. Soc. 355 (2003), pp. 2523–2543] 主要结果的改进，其中定理在 $\ mathscr {T}$ 有一个足够好的模型。应该提到的是，Alonso、Jeremías 和 Souto 的结果具有影响力——研究所有这些 $t$-结构很有趣。

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