Geodesic
On the Étale K-Theory of an Elliptic Curve with Complex Multiplication for Regular Primes
Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 145-150

Voir la notice de l'article provenant de la source Cambridge University Press

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.,
DOI : 10.4153/CMB-1990-025-x
Mots-clés : 11G05, 19E08, 19E20 
Wingberg, Kay. On the Étale K-Theory of an Elliptic Curve with Complex Multiplication for Regular Primes. Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 145-150. doi: 10.4153/CMB-1990-025-x
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[1] 1. Dwyer, W. and Friedlander, E., Algebraic and étale K-theory, Trans. Amer. Math. Soc. 292 (1985), 247–280. Google Scholar

[2] 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] 3. Koch, H., Galoissche Théorie der p-Erweiterungen, Berlin 1970. Google Scholar

[4] 4. Neukirch, J., Freie Produkte proendlicher Gruppen und ihre Kohomologie, Archiv der Math. 22 (1972), 337–357. Google Scholar

[5] 5. Neukirch, J., Einbettungsprobleme mit lokaler Vorgabe und freie Produkte lokaler Gruppen, J. reine und angew. Math. 259 (1973), 1–47. Google Scholar

[6] 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] 7. Schneider, P., Über gewisse Galoiscohomologiegruppen, Math. Z. 168, (1979), 181–205. Google Scholar

[8] 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] 9. Soulé, C., p-adic k-theory of elliptic curves, Duke Math. J. 54 (1987), 249–269. Google Scholar

[10] 10. Wingberg, K., Ein Analogon zur Fundamental g ruppe einer Riemann’ schen Fläche im Zahlkörperfall, Invent, math. 77 (1984), 557–584. Google Scholar

[11] 11. Yager, R., A Kummer critérium for imaginary quadratic fields, Compositio Math. 47 (1982), 31–42. Google Scholar

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