Borel-Moore homology

General Introduction

See also Borel-Moore motivic homology

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Online References

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Paper References

Borel and Moore: Homology theory for locally compact spaces (Michigan Math. J., vol.7, 1960).

Chapter IX of Iversen: Cohomology of Sheaves, in Homol alg folder

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Definition

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Properties

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Standard theorems

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Open Problems

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Connections to Number Theory

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Computations and Examples

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History and Applications

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Some Research Articles

Kahn: We prove some finiteness theorems for the \'etale cohomology, Borel-Moore homology and cohomology with proper supports of schemes of finite type over a finite or p-adic field. This yields vanishing results for their l-adic cohomology, proving part of a conjecture of Jannsen.

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General Introduction