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

Rognes, J.; Weibel, C.; M. Kolster, appendix by

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

Two-primary algebraic $K$-theory of rings of integers in number fields
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by J. Rognes, C. Weibel and appendix by M. Kolster

J. Amer. Math. Soc. 13 (2000), 1-54

DOI: https://doi.org/10.1090/S0894-0347-99-00317-3

Published electronically: August 23, 1999

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Abstract:

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.

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