## New answers tagged derived-categories

2
votes

### How to conclude the quasi-projective case of the derived McKay correspondence from the projective case?

Paragraph 3.2 explains that duality still works for quasi-projective non-singular varieties if you restrict to the appropriate categories. Also I think there should be no particular problem with a ...

3
votes

### derived completion and flat base change

It is always a (quasi-)isomorphism.
In fact, because you are deriving the tensor product you do not need to assume $B$ is flat, and you do not need any assumptions on $A,B,f$, or even to assume that $...

4
votes

### Does there exist a faithful exact embedding of $D^b(\dim(N)) \to D^b(\dim(N-1))$

If you're not assuming full you can use Prop. 2.3 in
Canonaco, Alberto; Stellari, Paolo, Non-uniqueness of Fourier-Mukai kernels, Math. Z. 272, No. 1-2, 577-588 (2012). ZBL1282.14033.
to prove the ...

2
votes

### Does there exist a faithful exact embedding of $D^b(\dim(N)) \to D^b(\dim(N-1))$

This is answered by Noah Olander in Fully Faithful Functors and Dimension.

10
votes

Accepted

### Derived category of local systems of finite type on a $K(\pi,1)$ space: an explicit counterexample

I can give an example that is even a smooth complex algebraic variety that shows up naturally in algebraic geometry.
Let $X$ be the moduli space of abelian varieties of genus $g>1$ with full level $...

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