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Abelian curves of 2-power conductor

Published online by Cambridge University Press:  24 October 2008

A. P. Ogg
A. P. Ogg
Affiliation:
Department of Pure Mathematics, Cambridge University
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Extract

Let Q be the field of rational numbers, and let A be an Abelian curve (an Abelian variety of dimension one) defined over Q. Following Weil, the conductor of A is

where p runs over all primes, and the exponent is explained below; the primes dividing N are exactly those for which A has degenerate reduction modulo p.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 143 - 148
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Néron, A.Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Inst. Hautes Éitudes Sci. Publ. Math. No. 21 (1964).CrossRefGoogle Scholar
(2)Ogg, A. P. Elliptic curves and wild ramification (to appear).Google Scholar
(3)Tate, J. Elliptic functions over complete fields (unpublished).Google Scholar