Solvable Points on Projective Algebraic Curves

Author:

Pál Ambrus

Abstract

AbstractWe examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of degree prime to 6p defined over a solvable extension.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Period of the generic genus g curve via degeneration;Journal of Number Theory;2021-10

2. Solvable points on smooth projective varieties;Monatshefte für Mathematik;2015-07-21

3. Curves which do not Become Semi-Stable After any Solvable Extension;Rendiconti del Seminario Matematico della Università di Padova;2013

4. Solvable points on genus-one curves over local fields;Journal of the Institute of Mathematics of Jussieu;2012-05-16

5. Solvable points on genus one curves;Duke Mathematical Journal;2008-04-15

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