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Uniform bounds on the number of rational points of a family of curves of genus 2

✍ Scribed by L. Kulesz; G. Matera; E. Schost

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
357 KB
Volume
108
Category
Article
ISSN
0022-314X

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✦ Synopsis

We exhibit a genus-2 curve C defined over QðTÞ which admits two independent morphisms to a rank-1 elliptic curve defined over QðTÞ: We describe completely the set of QðTÞ-rational points of the curve C and obtain a uniform bound on the number of Q-rational points of a rational specialization C t of the curve C for a certain (possibly infinite) set of values tAQ: Furthermore, for this set of values tAQ we describe completely the set of Q-rational points of the curve C t : Finally, we show how these results can be strengthened assuming a height conjecture of Lang.

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