Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T04:23:39.887Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Étale K-Theory of an Elliptic Curve with Complex Multiplication for Regular Primes

Published online by Cambridge University Press:  20 November 2018

Kay Wingberg
Kay Wingberg*
Affiliation:
Mathematisches Institut, der Universität Heidelberg, D - 6900 Heidelberg, West-Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Generalizing a result of Soulé we prove that for an elliptic curve E defined over an imaginary quadratic field K with complex multiplication having good ordinary reduction at the prime number p > 3 which is regular for E and the extension F of K contained in K(Ep) the dimensions of the étale K-groups are equal to the numbers predicted by Bloch and Beilinson, i.e.,

Keywords

11G0519E0819E20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 145 - 150
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Dwyer, W. and Friedlander, E., Algebraic and étale K-theory, Trans. Amer. Math. Soc. 292 (1985), 247–280.Google Scholar
2. Jannsen, U., On the l-adic cohomology of varieties over number fields and its Galois cohomology, In: Galois groups over Q, ed. by Y. Ihara et al. MSRI Publ. Springer, (1989), 315–360.Google Scholar
3. Koch, H., Galoissche Théorie der p-Erweiterungen, Berlin 1970.Google Scholar
4. Neukirch, J., Freie Produkte proendlicher Gruppen und ihre Kohomologie, Archiv der Math. 22 (1972), 337–357.Google Scholar
5. Neukirch, J., Einbettungsprobleme mit lokaler Vorgabe und freie Produkte lokaler Gruppen, J. reine und angew. Math. 259 (1973), 1–47.Google Scholar
6. Neumann, O., On p-closed number fields and an analogue of Riemann s existence theorem, In: A. Fröhlich, Algebraic number fields, London 1977, 625–647.Google Scholar
7. Schneider, P., Über gewisse Galoiscohomologiegruppen, Math. Z. 168, (1979), 181–205.Google Scholar
8. Soulé, C., The rank of étale cohomology of varieties over p-adic or number fields, Compositio Math. 53(1984), 113–131.Google Scholar
9. Soulé, C., p-adic k-theory of elliptic curves, Duke Math. J. 54 (1987), 249–269.Google Scholar
10. Wingberg, K., Ein Analogon zur Fundamental g ruppe einer Riemann’ schen Fläche im Zahlkörperfall, Invent, math. 77 (1984), 557–584.Google Scholar
11. Yager, R., A Kummer critérium for imaginary quadratic fields, Compositio Math. 47 (1982), 31–42.Google Scholar