We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

On the non-commutative main conjecture for elliptic curves with complex multiplication.

Bouganis, A. and Venjakob, O. (2010) 'On the non-commutative main conjecture for elliptic curves with complex multiplication.', Asian journal of mathematics., 14 (3). pp. 385-416.


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.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
Full text:Publisher-imposed embargo
(VoR) Version of Record
File format - PDF
Publisher Web site:
Date accepted:20 August 2010
Date deposited:11 April 2017
Date of first online publication:September 2010
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar