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

Rognes, J.¹ ; Weibel, C.² ; M. Kolster, appendix by³

¹ Department of Mathematics, University of Oslo, Oslo, Norway
² Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
³ Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

Journal of the American Mathematical Society, Tome 13 (2000) no. 1, pp. 1-54

Résumé

We relate the algebraic $K$-theory of the ring of integers in a number field $F$ to its étale cohomology. We also relate it to the zeta-function of $F$ when $F$ is totally real and Abelian. This establishes the $2$-primary part of the “Lichtenbaum conjectures.” To do this we compute the $2$-primary $K$-groups of $F$ and of its ring of integers, using recent results of Voevodsky and the Bloch–Lichtenbaum spectral sequence, modified for finite coefficients in an appendix. A second appendix, by M. Kolster, explains the connection to the zeta-function and Iwasawa theory.

Détail

DOI : 10.1090/S0894-0347-99-00317-3

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