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Algebraic K-theory and the norm-residue homomorphism

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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 isomorphismR n,F :K 2(F)/nK 2(F) ∼→ n Br(F). Algebrogeometric applications of the main results are presented.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki Noveishie Dostizheniya, Vol. 25, pp. 115–208, 1984.

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Suslin, A.A. Algebraic K-theory and the norm-residue homomorphism. J Math Sci 30, 2556–2611 (1985). https://doi.org/10.1007/BF02249123

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