TWO-COVER DESCENT ON HYPERELLIPTIC CURVES

被引：47

作者：

Bruin, Nils ^{[1
]}

Stoll, Michael ^{[2
]}

机构：

[1] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

[2] Univ Bayreuth, Math Inst, D-95440 Bayreuth, Germany

来源：

MATHEMATICS OF COMPUTATION | 2009年 / 78卷 / 268期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Local-global obstruction; rational points; hyperelliptic curves; descent; RATIONAL-POINTS; ALGEBRAIC-CURVES; JACOBIANS; CHABAUTY;

D O I：

10.1090/S0025-5718-09-02255-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns an empty set, then the hyperelliptic curve has no rational points. This provides a relatively efficiently tested criterion for solvability of hyperelliptic curves. We also discuss applications of this algorithm to curves of genus I and to curves with rational points.

引用

页码：2347 / 2370

页数：24

共 26 条

[11] Deciding existence of rational points on curves: An experiment [J].

Bruin, Nils ;

Stoll, Michael .

EXPERIMENTAL MATHEMATICS, 2008, 17 (02) :181-189

[12]

BRUIN NR, 1999, THESIS U LEIDEN LEID

[13]

Chabauty C, 1941, CR HEBD ACAD SCI, V212, P882

[14]

Chevallev C, 1932, CR HEBD ACAD SCI, V195, P570

[15] EFFECTIVE CHABAUTY [J].

COLEMAN, RF .

DUKE MATHEMATICAL JOURNAL, 1985, 52 (03) :765-770

[16] A flexible method for applying Chabauty's Theorem [J].

Flynn, EV .

COMPOSITIO MATHEMATICA, 1997, 105 (01) :79-94

[17] Finding rational points on bielliptic genus 2 curves [J].

Flynn, EV ;

Wetherell, JL .

MANUSCRIPTA MATHEMATICA, 1999, 100 (04) :519-533

[18]

Merriman JR, 1996, ACTA ARITH, V77, P385

[19]

Poonen B, 1997, J REINE ANGEW MATH, V488, P141

[20] The Cassels-Tate pairing on polarized abelian varieties [J].

Poonen, B ;

Stoll, M .

ANNALS OF MATHEMATICS, 1999, 150 (03) :1109-1149

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