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Galois groups of number fields generated by torsion points of elliptic curves

Published online by Cambridge University Press:  22 January 2016

Kay Wingberg
Kay Wingberg*
Affiliation:
NWF I—Mathematik der Universität Regensburg Universitätsstraße 31, D-84-00 Regensburg, F.R.G.
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Coates and Wiles [1] and B. Perrin-Riou (see [2]) study the arithmetic of an elliptic curve E defined over a number field F with complex multiplication by an imaginary quadratic field K by using p-adic techniques, which combine the classical descent of Mordell and Weil with ideas of Iwasawa’s theory of Zp-extensions of number fields. In a special case they consider a non-cyclotomic Zp-extension F∞ defined via torsion points of E and a certain Iwasawa module attached to E/F, which can be interpreted as an abelian Galois group of an extension of F∞. We are interested in the corresponding non-abelian Galois group and we want to show that the whole situation is quite analogous to the case of the cyclotomic Zp-extension (which is generated by torsion points of Gm).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 104 , December 1986 , pp. 43 - 53
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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