实封闭的域上椭圆曲线的单基性与约化
One-basedness and reductions of elliptic curves over real closed fields
摘要：
在Pillay猜想正解的基础上，提出了实封闭的域K上椭圆曲线的“内禀”约化概念.我们将这一概念与传统的代数几何约化进行了比较，并根据E的代数几何约化方式和“内在”约化曲线的几何复杂性，给出了具有三个“实”根的椭圆曲线E的K点群的分类。
英文摘要：
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.
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