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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| - ノルム剰余同型定理 (ja)
- Norm residue isomorphism theorem (en)
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| - 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)
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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 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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