nLab derived category of coherent sheaves

Idea

The derived category of a category quasi-coherent sheaves.

Related concepts

• derived category

• coherent sheaves

• Bondal-Orlov reconstruction theorem

• Fourier-Mukai transform

• triangulated categories of sheaves

• Bridgeland stability condition

References

General

• A. I. Bondal, D. O. Orlov, Derived categories of coherent sheaves, Proc. Internat. Congress of Mathematicians vol. II 46–54 (Beijing, 2002)

  djvu:134K pdf:881K

• V. A. Lunts, D. O. Orlov, Uniqueness of enhancement for triangulated categories, J. Amer. Math. Soc. 23 (2010), 853-908, journal, arXiv:0908.4187, doi

• Dmitri Orlov, Derived categories of coherent sheaves and motives.

  math.AG/0512620

• Dmitri Orlov, Derived categories of coherent sheaves and triangulated categories of singularities, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II, 503–531, Progr. Math., 270, Birkhauser, Boston, Inc., Boston, MA, 2009 math.AG/0503632

• A. N. Kapustin, D. O. Orlov, Lectures on mirror symmetry, derived categories, and D-branes (Russian) Uspekhi Mat. Nauk 59 (2004), no. 5 (359), 101–134; English translation in Russian Math. Surveys 59 (2004), no. 5, 907–940 math.AG/0308173

• A. I. Bondal, D. O. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compos. Math. 125 (2001), 327–344 doi:10.1023/A:1002470302976

• L.Katzarkov, M.Kontsevich, T.Pantev, Hodge theoretic aspects of mirror symmetry, arxiv:0806.0107

• Valery Lunts, Olaf M. Schnuerer, New enhancements of derived categories of coherent sheaves and applications, arXiv.

Introduction and review:

• Franco Rota, The derived categories of coherent sheaves, lecture notes [pdf, pdf]

In Rozansky-Witten theory

On Rozansky-Witten weight systems as Lie algebra weight systems for Lie algebra objects in the derived category of quasi-coherent sheaves, and unified Wheels theorem:

• Justin Roberts, Simon Willerton, On the Rozansky-Witten weight systems, Algebr. Geom. Topol. 10 (2010) 1455-1519 (arXiv:math/0602653)

Related concepts

• B-modeltopological string

References

On t-structures on derived categories of coherent sheaves:

• Dan Abramovich, Alexander Polishchuk, Sheaves of t-structures and valuative criteria for stable complexes, J. reine angew. Math. 590 (2006) 89-130 [arXiv:math/0309435, doi:10.1515/CRELLE.2006.005]

• Alexander Polishchuk, Constant families of t-structures on derived categories of coherent sheaves, Moscow Math. J. 7 (2007) 109-134 [arXiv:math/0606013]