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Preprint Number 486
486. Davide Penazzi
One-basedness and reductions of elliptic curves over real closed fields
Submission date: 3 August 2012.
Building on the positive solution of Pillay's conjecture we present a notion of intrinsic reduction for elliptic curves over a real closed field K. We compare such notion with the traditional algebro-geometric reduction and produce a classification of the group of K-points of an elliptic curve E with three real roots according to the way E reduces (algebro-geometrically) and the geometric complexity of the intrinsically reduced curve.
Mathematics Subject Classification: 03C45, 03C98, 12J10, 14H52
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