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Penazzi, Davide 
ORCID: 0000-0002-9732-1577
(2014)
One-basesness and reductions of elliptic curves over real closed fields.
Transactions of the American Mathematical Society (TRAN), 367
.
pp. 1827-1845.
ISSN 0002-9947
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Official URL: https://doi.org/10.1090/S0002-9947-2014-06099-6
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 a 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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