Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T17:33:15.565Z Has data issue: false hasContentIssue false
  • English
  • Français

Iwasawa Theory for K2n

Published online by Cambridge University Press:  02 May 2013

Qingzhong Ji  and
Hourong Qin
Qingzhong Ji
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, [email protected]
Hourong Qin
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, [email protected]
Get access

Abstract

Given a number field F and a prime number p; let Fn denote the cyclotomic extension with [Fn : F] = pn; and let denote its ring of integers. We establish an analogue of the classical Iwasawa theorem for the orders of K2i (){p}.

Keywords

Higher K-groupsℤp-extensionIwasawa theory11R1811R2311R7019F27
Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 115 - 123
Copyright
Copyright © ISOPP 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Borel, A., Cohomologie reele stable des groupes S-arithmetiques classiques, C.R. Acad. Sci. Paris 271 (1970), 1156–1158.Google Scholar
2.Coates, J., On K 2 and classical conjectures in algebraic number theory, Ann. Math. 95 (1972), 99–116.Google Scholar
3.Dwyer, W. and Friedlander, E., Algebraic and étale K-theory, Trans. AMS 292 (1985), 247–280.Google Scholar
4.Iwasawa, K., On ℤl-extensions of algebraic number fields, Ann. Math. 98(1973), 246–326.CrossRefGoogle Scholar
5.Do, T. Nguyen Quang, Sur la ℤp-torsion de certains modules galoisiens, Ann. Inst. Fourier, 36(2) (1986), 27–46.Google Scholar
6.Quillen, D., Finite generation of the groups Ki of rings of algebraic integers, Lecture Notes in Math. 341 (1973), 179–198.CrossRefGoogle Scholar
7.Rognes, J. and Weibel, C., Two-primary algebraic K-theory of rings of integers in number fields, J. AMS 13 (2000), 1–54.Google Scholar
8.Schneider, P., Über gewisse Galois cohomologie gruppen, Math. Z. 168 (1979), 181–205.CrossRefGoogle Scholar
9.Soule, C., On higher p-adic regulators, Lecture Notes in Math. 854 (1981), 372–401.Google Scholar
10.Weibel, C., Étale Chern classes at the prime 2, Algebraic K-theory and Algebraic Topology, Editors: P. Goerss and J. F. Jardine, NATO ASI Series C 407, Kluwer, 1993, 249–286.CrossRefGoogle Scholar
11.Weibel, C., Algebraic K-theorey of Rings of Integers in Local and Global Fields, in Handbook of K-theory, Editors: E.M. Friedlander and D. R. Grayson, Springer-Verlag, New York, 2005, 139–190.Google Scholar
12.Weibel, C., The 2-torsion in the K-theory of integers, C. R. Acad. Sci. Paris 324 (1997), 615–620.Google Scholar
13.Weibel, C., The K-book: an introduction to Algebraic K-theory, GSM 145, AMS, 2013.Google Scholar