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A note on elliptic curves and Galois module structure in global function fields
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 118, Number 2, April 1996
- pp. 427-438
- 10.1353/ajm.1996.0010
- Article
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In this paper we study the Galois module structure of certain Kummer orders obtained by dividing torsion points on an elliptic curve defined over a global function field. We prove that such Kummer orders are globally free as Galois modules. This is the analogue over function fields of a conjecture first stated by M. J. Taylor for CM elliptic curves defined over number fields.