Two-primary algebraic 𝐾-theory of rings of integers in number fields

DOI10.1090/S0894-0347-99-00317-3zbMath0934.19001OpenAlexW1507724797MaRDI QIDQ4700177

John Rognes, Charles A. Weibel

Publication date: 1 November 1999

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-99-00317-3

zbMATH Keywords

number fieldsétale cohomologymotivic cohomologyLichtenbaum conjectureBloch-Lichtenbaum spectral sequenceLichtenbaum-Quillen conjecturestwo-primary algebraic \(K\)-theory

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Computations of higher (K)-theory of rings (19D50) (K)-theory of global fields (11R70) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Motivic cohomology; motivic homotopy theory (14F42) (K)-theory of local fields (11S70)

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Cites Work

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• Class groups of abelian fields, and the main conjecture
• Homology of the infinite orthogonal and symplectic groups over algebraically closed fields. An appendix to the paper of A. Suslin
• Algebraic cycles and higher K-theory
• Continuous étale cohomology
• Über gewisse Galoiscohomologiegruppen
• K-théorie des anneaux d'entiers de corps de nombres et cohomologie etale
• \(K_i\) groups of rings of algebraic integers
• Étale descent for two-primary algebraic \(K\)-theory of totally imaginary number fields
• Two-primary algebraic \(K\)-theory of two-regular number fields
• On the groups \(J(X)\). IV
• On the cohomology and K-theory of the general linear groups over a finite field
• On the values of zeta and L-functions. I
• The Iwasawa conjecture for totally real fields
• Algebraic and Etale K-Theory
• Higher algebraic K-theory: I
• Stable real cohomology of arithmetic groups
• Continuous cohomology and p-adic K-theory
• The 2-torsion in the K-theory of the integers