Coates-Wiles towers for CM abelian varieties

Details Coates-Wiles towers for CM abelian varieties Coates-Wiles towers for CM abelian varieties

2004-04-02

arxiv.org/abs/math/0404022v1

Mathematics

Number Theory

23 pages, 2 figures

Scientific paper

Let A be a CM abelian variety defined over a number field K. We compute congruence relations on units in fields generated by adjoining torsion points of A to K. For elliptic curves, congruence relations of the type we compute were used in the proof of the Coates-Wiles theorem. In general, we compute congruence relations on exterior products of units in division fields. This result seems to fit more naturally into the framework of the Stark/Rubin conjectures.

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