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Coates-Wiles towers for CM abelian varieties

Christopher M. Rowe
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Abstract

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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Christopher M. Rowe. 2004-04-02. Coates-Wiles towers for CM abelian varieties. https://arxiv.org/abs/math/0404022

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