About: Norm residue isomorphism theorem

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In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation and at the same time represents the key juncture in the proofs of many seemingly unrelated theorems from abstract algebra, theory of quadratic forms, algebraic K-theory and the theory of motives. The theorem asserts that a certain statement holds true for any prime and any natural number . John Milnor speculated that this theorem might be true for and all , and this question became known as Milnor's conjecture. The general case was conjectured by Spencer Bloch and Kazuya Kato and became known as the Bloch–Kato conjecture or the motivic Bloch–Kato conjecture to distinguish it from the Bloch–Kato conjecture on values

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rdfs:label	ノルム剰余同型定理 (ja) Norm residue isomorphism theorem (en)
rdfs:comment	数学において、ノルム剰余同型定理 (norm residue isomorphism theorem)またはブロック・加藤予想 (Bloch-Kato conjecture) は、ミルナーのK-理論とガロアコホモロジーを結びつける、長らく予想されていた定理である。ジョン・ミルナー (John Milnor)はこの定理がの場合に正しいと予想し、これはミルナー予想として知られるようになった。一般の場合はと加藤和也により予想され、ブロック・加藤予想 (Bloch–Kato conjecture) 、もしくは（L-函数の特殊値におけるブロック・加藤の予想と区別するために）モチーフ的ブロック・加藤予想 (motivic Bloch–Kato conjecture) として知られるようになった。ノルム剰余同型定理はウラジミール・ヴォエヴォツキー (Vladimir Voevodsky) により、(Markus Rost)の数々の斬新な結果を用いて証明された。 (ja) In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation and at the same time represents the key juncture in the proofs of many seemingly unrelated theorems from abstract algebra, theory of quadratic forms, algebraic K-theory and the theory of motives. The theorem asserts that a certain statement holds true for any prime and any natural number . John Milnor speculated that this theorem might be true for and all , and this question became known as Milnor's conjecture. The general case was conjectured by Spencer Bloch and Kazuya Kato and became known as the Bloch–Kato conjecture or the motivic Bloch–Kato conjecture to distinguish it from the Bloch–Kato conjecture on values (en)
rdfs:seeAlso	Quillen–Lichtenbaum conjecture
dcterms:subject	Algebraic K-theory Theorems in algebraic topology Conjectures that have been proved Theorems in algebra
Wikipage page ID	27126857 (xsd:integer)
Wikipage revision ID	1109463881 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Multiplicative group Morava K-theory Motivic homotopy theory Algebraic cobordism Algebraic K-theory Vladimir Voevodsky Thom space Mathematics Quillen–Lichtenbaum conjecture Special values of L-functions Milnor K-theory Andrei Suslin Étale cohomology Theorems in algebraic topology Two-sided ideal Galois cohomology Local class field theory American Mathematical Society Field (mathematics) Brauer group Charles Weibel Hilbert's Theorem 90 Hilbert symbol Journal of Topology Conjectures that have been proved Theorems in algebra John Milnor Kazuya Kato Birkhäuser Eilenberg–MacLane space Model category Spencer Bloch Markus Rost Tensor algebra Steenrod algebra Milnor conjecture Motivic cohomology Norm residue isomorphism theorem Spanier–Whitehead duality Milnor's conjecture dbr:Motivic_Steenrod_algebra dbr:Algebraic_Morava_K-theories dbr:Seva_Joukhovitski dbr:Simone_Borghesi
Link from a Wikipage to an external page	http://www.math.uiuc.edu/K-theory/0170 http://www.numdam.org/item%3Fid=PMIHES_2003__98__1_0 http://www.math.uiuc.edu/K-theory/0412 http://annals.math.princeton.edu/2011/174-1/p11%7Carxiv=0805.4430 http://www.math.uni-bielefeld.de/~rost/chain-lemma.html https://www.researchgate.net/publication/225345330%7C
sameAs	Norm residue isomorphism theorem Norm residue isomorphism theorem Norm residue isomorphism theorem Norm residue isomorphism theorem Norm residue isomorphism theorem
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has abstract	In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation and at the same time represents the key juncture in the proofs of many seemingly unrelated theorems from abstract algebra, theory of quadratic forms, algebraic K-theory and the theory of motives. The theorem asserts that a certain statement holds true for any prime and any natural number . John Milnor speculated that this theorem might be true for and all , and this question became known as Milnor's conjecture. The general case was conjectured by Spencer Bloch and Kazuya Kato and became known as the Bloch–Kato conjecture or the motivic Bloch–Kato conjecture to distinguish it from the Bloch–Kato conjecture on values of L-functions. The norm residue isomorphism theorem was proved by Vladimir Voevodsky using a number of highly innovative results of Markus Rost. (en) 数学において、ノルム剰余同型定理 (norm residue isomorphism theorem)またはブロック・加藤予想 (Bloch-Kato conjecture) は、ミルナーのK-理論とガロアコホモロジーを結びつける、長らく予想されていた定理である。ジョン・ミルナー (John Milnor)はこの定理がの場合に正しいと予想し、これはミルナー予想として知られるようになった。一般の場合はと加藤和也により予想され、ブロック・加藤予想 (Bloch–Kato conjecture) 、もしくは（L-函数の特殊値におけるブロック・加藤の予想と区別するために）モチーフ的ブロック・加藤予想 (motivic Bloch–Kato conjecture) として知られるようになった。ノルム剰余同型定理はウラジミール・ヴォエヴォツキー (Vladimir Voevodsky) により、(Markus Rost)の数々の斬新な結果を用いて証明された。 (ja)
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page length (characters) of wiki page	17023 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Norm_residue_isomorphism_theorem

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