Derived categories of coherent sheaves
Alexei Bondal, Dmitri Orlov
TL;DR
This paper explores how derived categories serve as a unifying framework connecting various areas of mathematics such as geometry, algebra, and noncommutative structures through semiorthogonal decompositions.
Contribution
It introduces the concept of semiorthogonal decompositions as fundamental tools for understanding the structure of derived categories across different mathematical contexts.
Findings
Semiorthogonal decompositions facilitate the analysis of derived categories.
Derived categories link geometric and algebraic structures.
The framework unifies commutative and noncommutative mathematics.
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory