Singular support of a coherent sheaf

Definition

Let $Y$ be a quasi-smooth derived scheme or stack, and let $\operatorname{Sing}(Y)$ be its classical scheme of singularities. The singular support of a coherent complex $\mathcal F$ is a closed conical subset

defined by the action of cohomological operators associated with the derived normal directions of $Y$.

For a conical closed subset $Z\subseteq\operatorname{Sing}(Y)$, the full subcategory $\operatorname{IndCoh}_Z(Y)$ consists of ind-coherent sheaves whose singular support is contained in $Z$.

This derived-algebraic notion is distinct from the singular support of a distribution or the microsupport of a constructible sheaf.