On the non-commutative Local Main Conjecture for elliptic curves with complex multiplication

Details On the non-commutative Local Main Conjecture for elliptic curves with complex multiplication On the non-commutative Local Main Conjecture for elliptic curves with complex multiplication

2012-04-19

arxiv.org/abs/1204.4269v1

Mathematics

Number Theory

39 pages

Scientific paper

This paper is a natural continuation of the joint work [6] on non-commutative Main Conjectures for CM elliptic curves: now we concentrate on the local Main Conjecture or more precisely on the epsilon-isomorphism conjecture by Fukaya and Kato in [20]. Our results rely heavily on Kato's unpublished proof of (commutative) epsilon-isomorphisms for one dimensional representations of G_{Q_p} in [24]. For the convenience of the reader we give a slight modification or rather reformulation of it in the language of [20] and extend it to the (slightly non-commutative) semi-global setting.

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