The dimension of fields and algebraic \(K\)-theory

DOI10.1016/0022-314X(86)90105-8zbMath0608.12029OpenAlexW2017685872MaRDI QIDQ1086294

Takako Kuzumaki, Kazuya Kato

Publication date: 1986

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(86)90105-8

zbMATH Keywords

Galois cohomologyprofinite groupnorm maps\(C_i\)-fieldcohomological p-dimensionMilnor's K-theorystability for higher K-theory

Mathematics Subject Classification ID

Cohomological dimension of fields (12G10) Galois cohomology (12G05) (K)-theory of global fields (11R70) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) (K)-theory of local fields (11S70) (K)-theory in number theory (19F99) Karoubi-Villamayor-Gersten (K)-theory (19D25)

Related Items (13)

Homogeneous spaces, algebraic \(K\)-theory and cohomological dimension of fields ⋮ Galois Cohomology of Unipotent Algebraic Groups and Field Extensions ⋮ On a conjecture of Kato and Kuzumaki ⋮ Duality via cycle complexes ⋮ Fields of dimension one algebraic over a global or local field need not be of type \(C_1\) ⋮ On the cohomology of reciprocity sheaves ⋮ Unnamed Item ⋮ On Kato and Kuzumaki's properties for the Milnor \(K_2\) of function fields of \(p\)-adic curves ⋮ Reduced norms of division algebras over complete discrete valuation fields of local-global type ⋮ On the Rost divisibility of henselian discrete valuation fields of cohomological dimension 3 ⋮ On the \(p\)-dimension of fields ⋮ Special fibre of low degree hypersurfaces ⋮ Unnamed Item

Cites Work

• Quadratic forms over semilocal rings
• Unramified class field theory of arithmetical surfaces
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. 3ième éd.
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• Pfister forms and \(K\)-theory of fields
• On quasi algebraic closure
• $ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM
• Duality in the flat cohomology of a surface
• Rational points in Henselian discrete valuation rings
• A field of cohomological dimension 1 which is not $C_1$
• Introduction to Algebraic K-Theory. (AM-72)
• Dimension cohomologique : Premiers resultats
• Quadratic forms over arbitrary fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The dimension of fields and algebraic \(K\)-theory