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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AT (Algebraic topology), AG (Algebraic geometry)
Mixed
See also Borel-Moore motivic homology
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
I think algebraic cobordism might be the universal oriented Borel-Moore homology.
nLab page on Borel-Moore homology