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$t$-structure is a structure imposed on triangulated categories, first introduced in Beilinson, Bernstein, Deligne's "Faisceaux Pervers".

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The derived category of the heart of a t-structure

Suppose $\mathcal{D}$ is a triangulated category and that we are given a $t$-structure $(\mathcal{D}^{\leq 0},\mathcal{D}^{\geq 0})$ on $\mathcal{D}$. The heart of the $t$-structure, $\mathcal{A}=\ma …
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