# The decomposition theorem, perverse sheaves and the topology of algebraic maps

```@article{Cataldo2009TheDT,
title={The decomposition theorem, perverse sheaves and the topology of algebraic maps},
author={Mark Andrea de Cataldo and Luca Migliorini},
journal={Bulletin of the American Mathematical Society},
year={2009},
volume={46},
pages={535-633}
}```
• Published 3 December 2007
• Mathematics
• Bulletin of the American Mathematical Society
We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the decomposition theorem, indicate some important applications and examples.
173 Citations

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