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One-basedness and reductions of elliptic curves over real closed fields


Author: Davide Penazzi
Journal: Trans. Amer. Math. Soc. 367 (2015), 1827-1845
MSC (2010): Primary 03C98, 14H52; Secondary 03C45, 12J10
DOI: https://doi.org/10.1090/S0002-9947-2014-06099-6
Published electronically: September 4, 2014
MathSciNet review: 3286500
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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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Additional Information

Davide Penazzi
Affiliation: School of Mathematics, University of Leeds, Leeds, LS2 9Jt, United Kingdom
Address at time of publication: School of Computing, Engineering and Physical Sciences, University of Lancashire, Leighton Building, Preston PR1 2HE, United Kingdom
Email: D.Penazzi@leeds.ac.uk, dpenazzi@uclan.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-2014-06099-6
Received by editor(s): October 12, 2011
Received by editor(s) in revised form: July 3, 2012, November 23, 2012, and February 4, 2013
Published electronically: September 4, 2014
Additional Notes: This research was supported by EPSRC grant EP/F009712/1
Article copyright: © Copyright 2014 American Mathematical Society