Derived categories of coherent sheaves

Abstract

We show how derived categories build bridges across the current mathematical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal decompositions of triangulated categories. To appear in the Proceedings of the ICM 2002 in Beijing.

ICM talk, 12 pp., LaTeX

References in corpus (3)

• Generators and representability of functors in commutative and noncommutative geometry
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• Francia's flip and derived categories

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