Let $X$ be something. (smooth and projective variety over C are my assumptions) The stack $M$ parameterising coherent sheaves on $X$ splits as a disjoint union of open and closed s …

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 $t$-structu …

Are there any good tricks to construct a heart of a t-structure? (I'm thinking on the derived category of coherent sheaves of some variety) I'll start with the only one I know. If …

By the Riemann-Hilbert correspondence, there is an equivalence between (1) $\mathcal{D}\operatorname{-mod}(X)$ , the (derived) category of holonomic D-modules on a complex v …

A thick subcategory of a triangulated category $C$ is essentially one that one can get away with declaring to be zero, i.e. it is the subcategory which sent to 0 when declares that …