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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 ...
Nicolas Hemelsoet's user avatar
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 $...
Maxime Ramzi's user avatar
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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 ...
AT0's user avatar
  • 1,417
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.
Sasha's user avatar
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10 votes

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 $...
Will Sawin's user avatar
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