Derived Categories of Coherent Sheaves
By A. Bondal, Dmitri Orlov. 2002
68 citations recorded by the source corpus.
We show how derived categories build bridges across the current mathe matical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal decompositions of triangulated categories.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d780385d12cdb4b7e5240a6b31c9eb0bd561d1de
How researchers see this paper
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In Geometry and Topology
- Amnon Yekutieli
- James J. Zhang
- Yukinobu Toda
- D. Kaledin
- T. Bridgeland
- Michel van den Bergh
- Emanuele Macrì
- Alexander Kuznetsov
In Mathematical Physics
- Amnon Yekutieli
- James J. Zhang
- Yukinobu Toda
- D. Kaledin
- T. Bridgeland
- Michel van den Bergh
- Emanuele Macrì
- P. Stellari
Citations in the corpus
- Derived Equivalences by Quantization (2005, background): “derived categories Db coh (X × Y U y) and Db coh (X ′× Y U y) are equivalent. This is a very particular case of [Ka, Conjecture 1.2], which in turn essentially goes back to [BO1, Section 3] (see also [BO2]). In the language of Y. Kawamata, “K-equivalence implies D-equivalence” (for symplectic resolu”
- Derived categories of coherent sheaves (2006, methodology): “The following conjecture was first made by Bondal and Orlov [5].”
- Dualizing complexes and perverse sheaves on noncommutative ringed schemes (2002, background): “der the role Grothendieck duality plays both in commutative algebraic geometry and in noncommutative ring theory. Furthermore, recent developments, mainly surrounding homological mirror symmetry (cf. [BO] and [Do]), tell us that there is a profound interplay between algebraic geometry, noncommutativ”