On the minimal set for counterexamples to the local–global principle

Resumen

Let p>3 be a prime number and let n   be a positive integer. We prove that the local–global principle for divisibility by pⁿ holds for elliptic curves defined over the rationals. For this, we refine our previous criterion for the validity of the principle. We also give an example that shows that the assumptions of our criterion are necessary.

Autores: Paladino, L., Ranieri, G., Viada, E.

Journal: Journal of Algebra

Journal Volume: 415

Journal Issue:

Journal Page: 290–304

Tipo de publicación: ISI

Fecha de publicación: 2014

Topics: Elliptic curves, Local–global divisibility problem

DOI: http://dx.doi.org/10.1016/j.jalgebra.2014.06.004

URL de la publicación: https://arxiv.org/pdf/1107.3431.pdf