On the local–global divisibility of torsion points on elliptic curves and GL2-type varieties
Let p be a prime number and let k be a number field. Let E be an elliptic curve defined over k. We prove that if p is odd, then the local–global divisibility by any power of p holds for the torsion points of E. We also show with an example that the hypothesis over p is necessary.
We get a weak generalization of the result on elliptic curves to the larger family of GL2-type varieties over k . In the special case of the abelian surfaces A/k with quaternionic multiplication over k we obtain that for all prime numbers p , except a finite number depending only on the isomorphism class of the ring Endk(A), the local–global divisibility by any power of p holds for the torsion points of A.
Autores: Gillibert, F., Ranieri, G.
Journal: Journal of Number Theory
Journal Volume: 174
Journal Page: 202-220
Tipo de publicación: Scopus
Fecha de publicación: 2017
Topics: Galois cohomology, Local–global, Elliptic curves, GL2-type varieties, Quaternionic multiplication
URL de la publicación: http://www.sciencedirect.com/science/article/pii/S0022314X16302943