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On the non-commutative Main Conjecture for elliptic curves with Complex Multiplication

Bouganis, A.; Venjakob, O.

Authors

O. Venjakob



Abstract

In [7] a non-commutative Iwasawa Main Conjecture for elliptic curves over Q has been formulated. In this note we show that it holds for all CM-elliptic curves E defined over Q. This was claimed in (loc. cit.) without proof, which we want to provide now assuming that the torsion conjecture holds in this case. Based on this we show firstly the existence of the (non-commutative) p-adic L-function of E and secondly that the (non-commutative) Main Conjecture follows from the existence of the Katz-measure, the work of Yager and Rubin’s proof of the 2-variable main conjecture. The main issues are the comparison of the involved periods and to show that the (non-commutative) p-adic L-function is defined over the conjectured in (loc. cit.) coefficient ring. Moreover we generalize our considerations to the case of CMelliptic cusp forms.

Citation

Bouganis, A., & Venjakob, O. (2010). On the non-commutative Main Conjecture for elliptic curves with Complex Multiplication. Asian Journal of Mathematics, 14(3), 385-416. https://doi.org/10.4310/ajm.2010.v14.n3.a6

Journal Article Type Article
Acceptance Date Aug 20, 2010
Publication Date Sep 1, 2010
Deposit Date Sep 18, 2013
Journal Asian Journal of Mathematics
Print ISSN 1093-6106
Electronic ISSN 1945-0036
Publisher International Press
Peer Reviewed Peer Reviewed
Volume 14
Issue 3
Pages 385-416
DOI https://doi.org/10.4310/ajm.2010.v14.n3.a6

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