Submission date: 3 August 2012.

Abstract:

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

Keywords and phrases:

Full text arXiv 1208.0708: pdf, ps.