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Iwasawa Theory for K2n

Published online by Cambridge University Press:  02 May 2013

Qingzhong Ji
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, [email protected]
Hourong Qin
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, [email protected]
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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}.

Type
Research Article
Copyright
Copyright © ISOPP 2013 

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References

1.Borel, A., Cohomologie reele stable des groupes S-arithmetiques classiques, C.R. Acad. Sci. Paris 271 (1970), 11561158.Google Scholar
2.Coates, J., On K 2 and classical conjectures in algebraic number theory, Ann. Math. 95 (1972), 99116.Google Scholar
3.Dwyer, W. and Friedlander, E., Algebraic and étale K-theory, Trans. AMS 292 (1985), 247280.Google Scholar
4.Iwasawa, K., On ℤl-extensions of algebraic number fields, Ann. Math. 98(1973), 246326.CrossRefGoogle Scholar
5.Do, T. Nguyen Quang, Sur la ℤp-torsion de certains modules galoisiens, Ann. Inst. Fourier, 36(2) (1986), 2746.Google Scholar
6.Quillen, D., Finite generation of the groups Ki of rings of algebraic integers, Lecture Notes in Math. 341 (1973), 179198.CrossRefGoogle Scholar
7.Rognes, J. and Weibel, C., Two-primary algebraic K-theory of rings of integers in number fields, J. AMS 13 (2000), 154.Google Scholar
8.Schneider, P., Über gewisse Galois cohomologie gruppen, Math. Z. 168 (1979), 181205.CrossRefGoogle Scholar
9.Soule, C., On higher p-adic regulators, Lecture Notes in Math. 854 (1981), 372401.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, 249286.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, 139190.Google Scholar
12.Weibel, C., The 2-torsion in the K-theory of integers, C. R. Acad. Sci. Paris 324 (1997), 615620.Google Scholar
13.Weibel, C., The K-book: an introduction to Algebraic K-theory, GSM 145, AMS, 2013.Google Scholar