[ABC et le principe de Hasse pour les tordues de courbes hyperelliptiques]
En supposant la conjecture ABC, nous utilisons un travail de Granville pour montrer qu'une courbe hyperelliptique de genre au moins trois a une infinité de tordues quadratiques, qui violent le principe de Hasse si et seulement si elle n'a pas de point de branchement hyperelliptique rationnel sur .
Conditionally on the ABC conjecture, we apply work of Granville to show that a hyperelliptic curve of genus at least three has infinitely many quadratic twists that violate the Hasse Principle iff it has no -rational hyperelliptic branch points.
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@article{CRMATH_2018__356_9_911_0,
author = {Clark, Pete L. and Watson, Lori D.},
title = {ABC and the {Hasse} principle for quadratic twists of hyperelliptic curves},
journal = {Comptes Rendus. Math\'ematique},
pages = {911--915},
publisher = {Elsevier},
volume = {356},
number = {9},
year = {2018},
doi = {10.1016/j.crma.2018.07.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.07.007/}
}
TY - JOUR AU - Clark, Pete L. AU - Watson, Lori D. TI - ABC and the Hasse principle for quadratic twists of hyperelliptic curves JO - Comptes Rendus. Mathématique PY - 2018 SP - 911 EP - 915 VL - 356 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.07.007/ DO - 10.1016/j.crma.2018.07.007 LA - en ID - CRMATH_2018__356_9_911_0 ER -
%0 Journal Article %A Clark, Pete L. %A Watson, Lori D. %T ABC and the Hasse principle for quadratic twists of hyperelliptic curves %J Comptes Rendus. Mathématique %D 2018 %P 911-915 %V 356 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.07.007/ %R 10.1016/j.crma.2018.07.007 %G en %F CRMATH_2018__356_9_911_0
Clark, Pete L.; Watson, Lori D. ABC and the Hasse principle for quadratic twists of hyperelliptic curves. Comptes Rendus. Mathématique, Tome 356 (2018) no. 9, pp. 911-915. doi : 10.1016/j.crma.2018.07.007. http://www.numdam.org/articles/10.1016/j.crma.2018.07.007/
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