Number theory
ABC and the Hasse principle for quadratic twists of hyperelliptic curves
Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 911-915.

Conditionally on the ABC conjecture, we apply work of Granville to show that a hyperelliptic curve C/Q of genus at least three has infinitely many quadratic twists that violate the Hasse Principle iff it has no Q-rational hyperelliptic branch points.

En supposant la conjecture ABC, nous utilisons un travail de Granville pour montrer qu'une courbe hyperelliptique C/Q 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 Q.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.07.007
Clark, Pete L. 1; Watson, Lori D. 1

1 Department of Mathematics, University of Georgia, Athens, GA 30606, United States
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Clark, Pete L.; Watson, Lori D. ABC and the Hasse principle for quadratic twists of hyperelliptic curves. Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 911-915. doi : 10.1016/j.crma.2018.07.007. http://archive.numdam.org/articles/10.1016/j.crma.2018.07.007/

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