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- Norm_residue_isomorphism_theorem abstract "In the mathematical field of algebraic K-theory, the norm residue isomorphism theorem is a long-sought result whose proof was completed in 2011. Its statement was previously known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato, or more precisely the motivic Bloch–Kato conjecture in some places, since there is another Bloch–Kato conjecture on values of L-functions. The title "norm residue" originally referred to the symbol taking values in the Brauer group of k (when the field contains all ℓ-th roots of unity). Its usage here isin analogy with standard local class field theory which identifies the result in terms of a "higher" class field theory, still being developed.It is a generalisation of the Milnor conjecture of K-theory, which was proved in the 1990s by Vladimir Voevodsky, the Milnor conjecture being the 2-primary part of the Bloch–Kato conjecture. The point of the conjecture is to equate the torsion in a K-group of a field F, algebraic information that is in general relatively inaccessible, with the torsion in a Galois cohomology group for F, which is in many cases much easier to compute. The Merkurjev–Suslin theorem is an intermediate result. Now that the complete proof of the Bloch–Kato conjecture has been announced, due to several mathematicians and contained in quite a number of papers, the result is also known as the Voevodsky–Rost theorem, for Voevodsky and Markus Rost. The norm residue isomorphism theorem implies the Quillen–Lichtenbaum conjecture.It is equivalent to a theorem whose statement was once referred to as the Beilinson–Lichtenbaum conjecture.".
- Norm_residue_isomorphism_theorem wikiPageExternalLink chain-lemma.html.
- Norm_residue_isomorphism_theorem wikiPageID "27126857".
- Norm_residue_isomorphism_theorem wikiPageRevisionID "596100395".
- Norm_residue_isomorphism_theorem hasPhotoCollection Norm_residue_isomorphism_theorem.
- Norm_residue_isomorphism_theorem subject Category:Algebraic_K-theory.
- Norm_residue_isomorphism_theorem subject Category:Conjectures.
- Norm_residue_isomorphism_theorem subject Category:Theorems_in_algebra.
- Norm_residue_isomorphism_theorem type Abstraction100002137.
- Norm_residue_isomorphism_theorem type Cognition100023271.
- Norm_residue_isomorphism_theorem type Communication100033020.
- Norm_residue_isomorphism_theorem type Concept105835747.
- Norm_residue_isomorphism_theorem type Conjectures.
- Norm_residue_isomorphism_theorem type Content105809192.
- Norm_residue_isomorphism_theorem type Hypothesis105888929.
- Norm_residue_isomorphism_theorem type Idea105833840.
- Norm_residue_isomorphism_theorem type Message106598915.
- Norm_residue_isomorphism_theorem type Proposition106750804.
- Norm_residue_isomorphism_theorem type PsychologicalFeature100023100.
- Norm_residue_isomorphism_theorem type Speculation105891783.
- Norm_residue_isomorphism_theorem type Statement106722453.
- Norm_residue_isomorphism_theorem type Theorem106752293.
- Norm_residue_isomorphism_theorem type TheoremsInAlgebra.
- Norm_residue_isomorphism_theorem comment "In the mathematical field of algebraic K-theory, the norm residue isomorphism theorem is a long-sought result whose proof was completed in 2011. Its statement was previously known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato, or more precisely the motivic Bloch–Kato conjecture in some places, since there is another Bloch–Kato conjecture on values of L-functions.".
- Norm_residue_isomorphism_theorem label "Norm residue isomorphism theorem".
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- Norm_residue_isomorphism_theorem sameAs Q7051622.
- Norm_residue_isomorphism_theorem sameAs Q7051622.
- Norm_residue_isomorphism_theorem sameAs Norm_residue_isomorphism_theorem.
- Norm_residue_isomorphism_theorem wasDerivedFrom Norm_residue_isomorphism_theorem?oldid=596100395.
- Norm_residue_isomorphism_theorem isPrimaryTopicOf Norm_residue_isomorphism_theorem.