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Results tagged with derived-categories
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user 46690
For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.
2
votes
0
answers
566
views
higher direct images of O(E)
I hope this is well known, I just could not work it out myself.
Say I have a variety X (smooth and projective over C is my usual setup) with a smooth subvariety Z. Let f: BL_Z(X) --> X be the blowup …
- 1,280
3
votes
1
answer
378
views
Reference for comparison of heart cohomology with standard cohomology
I'm looking for a reference for the following fact (which I believe to be true and should be easy for people who understand how spectral sequences arise from filtrations).
Let A,B be two hearts of …
- 1,280
1
vote
0
answers
165
views
Ext and cup products and subvarieties
I am trying to understand Remark 11.3 in Huybrechts's amazing book on derived categories (FM transforms in AG).
He starts with smooth projective varieties $j\colon Y \subset X$ and aims to describe t …
- 1,280
4
votes
Accepted
Morphism between Fourier-Mukai functors implies the morphism between kernels?
This is somewhat sad, but I think (part of) what we've learned from the whole triangulated-vs-dg story is the following pseudo-statement: the bare category of functors Fun(D(X),D(Y)) is the wrong thin …
- 1,280
6
votes
Derived category of a hypersurface
Maybe it's worth spelling out the easy case of projective space (and Veronese embedding).
Take the standard exceptional collection $<O,O(1),...,O(n)>.$
The derived category of a hypersurface X of deg …
- 1,280
12
votes
Accepted
Are $D^b_{coh}(X)$ and $D^b(Coh(X))$ derived equivalent?
For X noetherian this is still true. (Proposition 3.5 in Daniel Huybrechts' book)
- 3,779
0
votes
Equivariant derived category and invariant divisor
It would be nice to have that general statement, which looks very similar to the blowup formula.
I don't know if it holds. For curves (essentially over C) this was studied here http://arxiv.org/pdf/m …
- 1,280