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ELLIPTIC AND HYPERELLIPTIC CURVES OVER SUPERSIMPLE FIELDS

Published online by Cambridge University Press:  28 January 2004

AMADOR MARTIN-PIZARRO  and
ANAND PILLAY
AMADOR MARTIN-PIZARRO
Affiliation:
Department of Mathematics, University of Urbana–Champaign, 273 Altgeld Hall, MC-382, 1409 West Green Street, Urbana, IL 61801, USApamartin@math.uiuc.edu
ANAND PILLAY
Affiliation:
Department of Mathematics, University of Urbana–Champaign, 273 Altgeld Hall, MC-382, 1409 West Green Street, Urbana, IL 61801, USApillay@math.uiuc.edu
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Abstract

It is proved that if $F$ is an infinite field with characteristic different from $2$, whose theory is supersimple, and $C$ is an elliptic or hyperelliptic curve over $F$ with generic ‘modulus’, then $C$ has a generic $F$-rational point. The notion of generity here is in the sense of the supersimple field $F$.

Keywords

03C6012E3014H52
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 1 - 13
Copyright
The London Mathematical Society 2004

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