Geodesic
Solvable Points on Projective Algebraic Curves
Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 612-637

Voir la notice de l'article provenant de la source Cambridge University Press

We 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.
DOI : 10.4153/CJM-2004-028-0
Mots-clés : 14H25, 11D88 
Pál, Ambrus. Solvable Points on Projective Algebraic Curves. Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 612-637. doi: 10.4153/CJM-2004-028-0
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