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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[GL2]
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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 = {459--493},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {19D50 (14C15 19D45 19E08)},
MRNUMBER = {1738056},
MRREVIEWER = {Michel Gros},
DOI = {10.1007/s002220050014},
ZBLNUMBER = {0957.19003},
} -
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@article {GL, MRKEY = {1807268},
AUTHOR = {Geisser, Thomas and Levine, Marc},
TITLE = {The {B}loch-{K}ato conjecture and a theorem of {S}uslin-{V}oevodsky},
JOURNAL = {J. Reine Angew. Math.},
FJOURNAL = {Journal für die Reine und Angewandte Mathematik},
VOLUME = {530},
YEAR = {2001},
PAGES = {55--103},
ISSN = {0075-4102},
CODEN = {JRMAA8},
MRCLASS = {14F42 (14C35 19E15)},
MRNUMBER = {1807268},
MRREVIEWER = {R. T. Hoobler},
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} -
[kraines]
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@article {kraines, MRKEY = {0202136},
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} -
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[Milnor3]
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[SJ]
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[H3new] V. Voevodsky, "Triangulated categories of motives over a field," in Cycles, Transfers, and Motivic Homology Theories, Princeton, NJ: Princeton Univ. Press, 2000, vol. 143, pp. 188-238.
@incollection {H3new, MRKEY = {1764202},
AUTHOR = {Voevodsky, Vladimir},
TITLE = {Triangulated categories of motives over a field},
BOOKTITLE = {Cycles, Transfers, and Motivic Homology Theories},
SERIES = {Ann. of Math. Stud.},
VOLUME = {143},
PAGES = {188--238},
PUBLISHER = {Princeton Univ. Press},
ADDRESS = {Princeton, NJ},
YEAR = {2000},
MRCLASS = {14F42 (14C25)},
MRNUMBER = {1764202},
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} -
[Redpub]
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[MCpub]
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AUTHOR = {Voevodsky, Vladimir},
TITLE = {Motivic cohomology with {${\bf Z}/2$}-coefficients},
JOURNAL = {Publ. Math. Inst. Hautes Études Sci.},
FJOURNAL = {Publications Mathématiques. Institut de Hautes Études Scientifiques},
VOLUME = {98},
YEAR = {2003},
PAGES = {59--104},
ISSN = {0073-8301},
MRCLASS = {14F42 (12G05 19D45 19E15)},
MRNUMBER = {2031199},
MRREVIEWER = {Eric M. Friedlander},
DOI = {10.1007/s10240-003-0010-6},
ZBLNUMBER = {1057.14028},
} -
@misc{motcoh,
author = {Voevodsky, Vladimir},
TITLE = {On motivic cohomology with ${\bf {Z}}/l$-coefficients},
YEAR={2003},
URL={www.math.uiuc.edu/K-theory/639/},
} -
[SRFsub]
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FJOURNAL = {Journal of K-Theory. K-Theory and its Applications in Algebra, Geometry, Analysis \& Topology},
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[oversub]
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ISSN = {1865-2433},
MRCLASS = {14F42 (19E15)},
MRNUMBER = {2600283},
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DOI = {10.1017/is010001030jkt107},
ZBLNUMBER = {1194.14029},
} -
@article{Red2sub,
author = {Voevodsky, Vladimir},
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@misc{patching,
author={Weibel, C.},
TITLE={Patching the norm residue isomorphism theorem},
URL={www.math.uiuc.edu/K-theory/844/},
YEAR={2007},
}