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p-adic cocycles and their regulator maps

Published online by Cambridge University Press:  19 October 2010

Zacky Choo  and
Victor Snaith
Zacky Choo
Affiliation:
School of Mathematics, University of Sheffield, Sheffield S37RH, [email protected]
Victor Snaith
Affiliation:
School of Mathematics, University of Sheffield, Sheffield S37RH, [email protected]
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Abstract

We derive a power series formula for the p-adic regulator on the higher dimensional algebraic K-groups of number fields. This formula is designed to be well suited to computer calculations and to reduction modulo powers of p.

Keywords

p-adic regulatoralgebraic K-grouplocal field
Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 2 , October 2011 , pp. 241 - 249
Copyright
Copyright © ISOPP 2010

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References

1. Burgos Gil, J.I.: The Regulators of Beilinson and Borel; Centre de Récherches Mathématiques Monograph Sér. 15, A.M. Soc (2002).Google Scholar
2. Choo, Z., Mannan, W., Garcia-Sanchez, R. and Snaith, V.P.: Computer calculations of the Borel regulator I and II; arXiv:0908.3765v2[math.KT] 4 Sep 2009 and arXiv:0909.0883v1[math.KT] 4 Sep 2009Google Scholar
3. Hamida, N.: Description explicite du régulateur de Borel; C.R. Acad. Sci. Paris Sr. I Math. 330 (2000) 169–172.CrossRefGoogle Scholar
4. Hamida, N.: Le régulateur p-adique; C.R. Acad. Sci. Paris Sr. I Math. 342 (2006) 807–812.CrossRefGoogle Scholar
5. Huber, A. and Kings, G.: A p-adic analogue of the Borel regulator and the Bloch-Kato exponential map; preprint DFG-Forschergruppe Regensburg/Leipzig (2006).Google Scholar
6. Karoubi, M.: Homologie cyclique et régulateurs en K-théorie algébrique; C.R. Acad. Sci. Paris Sr. I Math. 297 (1983) no.10, 557–560.Google Scholar
7. Karoubi, M.: Homologie cyclique et K-théorie; Astérisque 149 (1987).Google Scholar
8. Lazard, M.: Groupes analytiques p-adiques; Pub. Math. I.H.E.S. 26 Paris (1965) 389–603.Google Scholar
9. Nesterenko, Yu.P. and Suslin, A.A.: Homology of the general linear group over a local ring and Milnor's K-theory; (Russian) Izv. Akad. Nauk. SSSR Ser. Mat. 53 (1989), no. 1, 121–146; translation in Math. USSR-Izv. 34 (1990) no. 1, 121-145.Google Scholar
10. Quillen, D.G.: Higher Algebraic K-theory I: Battelle K-theory Conf. 1972; Lecture Notes in Math. 371 (1973) 85–147.CrossRefGoogle Scholar
11. Quillen, D.G.: On the cohomology and K-theory of the general linear groups over a finite field; Annals of Math. 96 (1972) 552–586.CrossRefGoogle Scholar
12. Snaith, V.P.: Explicit Brauer Induction (with applications to algebra and number theory); Cambridge Studies in Advanced Math. 40 (1994) Cambridge University Press.Google Scholar
13. Snaith, V.P.: Local fundamental classes derived from higher dimensional K-groups; Proc. Great Lakes K-theory Conf., Fields Institute Communications Series 16 (A.M.Soc. Publications) 285–324 (1997).Google Scholar
14. Soulé, C.: On higher p-adic regulators; Springer-Verlag Lecture Notes in Mathematics 854 (1981) 372–401.Google Scholar
15. Tamme, G.: Comparison of the Karoubi regulator and the p-adic Borel regulator; preprint #17 (25 July 2007) DFG-Forschergruppe Regensburg/Leipzig.Google Scholar
16. Wagoner, J.B.: Continuous cohomology and p-adic K-theory; Springer-Verlag Lecture Notes in Mathematics 551 (1976) 241–248.Google Scholar