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Orders of the torsion of points of curves of genus 1

✍ Scribed by V. A. Dem'yanenko

Publisher: Springer US
Year: 1982
Tongue: English
Weight: 826 KB
Volume: 18
Category: Article
ISSN: 1573-8795
DOI: 10.1007/bf01763959

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Tate proved a theorem on rational points of torsors ("Torsors" means "Homogeneous spaces," in sequel we use "torsors" in this meaning) of \(T / K\), where \(K\) is a local field, \(T\) is a Tate curve. In this paper we extend the above theorem to the case where \(T\) is a twist of a Tate curve, and

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For an algebraic curve CÂK defined by y 2 =x p +a (a Â K p ) with relative genus ( p&1)Â2 and absolute genus 0, we prove that the Picard group of divisors of degree 0, denoted Pic 0 K (C), of a curve CÂK fixed by the action of the Galois group G= gal(K sep ÂK) has a finite number of K-rational point

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