Algebraic K-theory and the norm-residue homomorphism

A. A. Suslin

doi:10.1007/BF02249123

Algebraic K-theory and the norm-residue homomorphism

A. A. Suslin

Mathematics

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49 Scopus citations

Abstract

Recent results on the structure of the group K₂ of a field and its connections with the Brauer group are presented. The K-groups of Severi-Brauer varieties and simple algebras are computed. A proof is given of Milnor's conjecture that for any field F and natural number n > 1 there is the isomorphism R_n,F:K₂(F)/nK₂(F)_→^∼_nBr(F). Algebrogeometric applications of the main results are presented.

Original language	English (US)
Pages (from-to)	2556-2611
Number of pages	56
Journal	Journal of Soviet Mathematics
Volume	30
Issue number	6
DOIs	https://doi.org/10.1007/BF02249123
State	Published - Sep 1985

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/BF02249123

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abstract = "Recent results on the structure of the group K2 of a field and its connections with the Brauer group are presented. The K-groups of Severi-Brauer varieties and simple algebras are computed. A proof is given of Milnor's conjecture that for any field F and natural number n > 1 there is the isomorphism Rn,F:K2(F)/nK2(F)→∼nBr(F). Algebrogeometric applications of the main results are presented.",

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Algebraic K-theory and the norm-residue homomorphism

Abstract

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