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.References
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Bibliographic Information
- J. Rognes
- Affiliation: Department of Mathematics, University of Oslo, Oslo, Norway
- Email: rognes@math.uio.no
- C. Weibel
- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
- MR Author ID: 181325
- Email: weibel@math.rutgers.edu
- appendix by M. Kolster
- Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- Email: kolster@mcmail.CIS.McMaster.CA
- Received by editor(s): July 13, 1998
- Published electronically: August 23, 1999
- © Copyright 1999 American Mathematical Society
- Journal: J. Amer. Math. Soc. 13 (2000), 1-54
- MSC (2000): Primary 19D50; Secondary 11R70, 11S70, 14F20, 19F27
- DOI: https://doi.org/10.1090/S0894-0347-99-00317-3
- MathSciNet review: 1697095