Abstract
In this paper we prove the conjecture of Bloch and Kato which relates Milnor’s $K$theory of a field with its Galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the Nisnevich and étale topologies.

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@article {GL2, MRKEY = {1738056},
AUTHOR = {Geisser, Thomas and Levine, Marc},
TITLE = {The {$K$}theory of fields in characteristic {$p$}},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {139},
YEAR = {2000},
NUMBER = {3},
PAGES = {459493},
ISSN = {00209910},
CODEN = {INVMBH},
MRCLASS = {19D50 (14C15 19D45 19E08)},
MRNUMBER = {1738056},
MRREVIEWER = {Michel Gros},
DOI = {10.1007/s002220050014},
ZBLNUMBER = {0957.19003},
} 
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} 
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@incollection {H3new, MRKEY = {1764202},
AUTHOR = {Voevodsky, Vladimir},
TITLE = {Triangulated categories of motives over a field},
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@misc{motcoh,
author = {Voevodsky, Vladimir},
TITLE = {On motivic cohomology with ${\bf {Z}}/l$coefficients},
YEAR={2003},
URL={www.math.uiuc.edu/Ktheory/639/},
} 
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@article{Red2sub,
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@misc{patching,
author={Weibel, C.},
TITLE={Patching the norm residue isomorphism theorem},
URL={www.math.uiuc.edu/Ktheory/844/},
YEAR={2007},
}