Let $\mathcal T$ be a well generated triangulated category, and let $S\subset\mathcal T$ be a set of objects. We prove that there is a t-structure on $\mathcal T$ with ${ \mathcal T}^{ \leq0}=\overline{ \langle S\rangle}^{ (-\infty,0]}$. This article is an improvement on the main result of a 2003 article by Alonso, Jeremias and Souto---in that article the theorem was proved under the assumption that $\mathcal T$ has a nice enough model. It should be mentioned that the theorem of Alonso, Jeremias and Souto has been influential---it turns out to be interesting to study all of these t-structures.
Categories: math.CT math.RT
