For a morphism of quasi-coherent sheaves $v\colon E \to F$, on a scheme $X$, one can ask about the locus where $v =0$. When $F$ is a vector bundle, it's easy to see that this locus is closed.* Is ...
Suppose I have a smooth projective variety $X$ and a semi-orthogonal decomposition of its bounded derived category of coherent sheaves $D^b(X)$. Then I can apply right or left mutations to the full ...
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 $(T,F)$ is a ...
The question is in the title. I am trying to apply the Mitchell (Freyd-Mitchell?) embedding theorem, which states that for every small abelian category $A$, there exists a ring $R$ such that A ...
Derived categories of (coherent) sheaves of modules: exceptional images, gluing, and proper descent?
I am interested in the properties of (the derived categories) of various categories of (coherent) sheaves of modules (over varieties). I would like to understand in what extent these properties are ...