Prescribing valuations of the order of a point in the reductions of abelian varieties and tori
| dc.creator | Perucca, Antonella | |
| dc.date | 2007-12-17 | |
| dc.date | 2008-10-11 | |
| dc.date.accessioned | 2026-07-07T10:08:50Z | |
| dc.date.available | 2026-07-07T10:08:50Z | |
| dc.description | Let G be the product of an abelian variety and a torus defined over a number field K. Let R be a K-rational point on G of infinite order. Call n_R the number of connected components of the smallest algebraic K-subgroup of G to which R belongs. We prove that n_R is the greatest positive integer which divides the order of (R mod p) for all but finitely many primes p of K. Furthermore, let m>0 be a multiple of n_R and let S be a finite set of rational primes. Then there exists a positive Dirichlet density of primes p of K such that for every l in S the l-adic valuation of the order of (R mod p) equals v_l(m). | |
| dc.description | Final version. To appear on Journal of Number Theory | |
| dc.identifier | https://arxiv.org/abs/0712.2812 | |
| dc.identifier | http://arxiv.org/abs/0712.2812 | |
| dc.identifier | doi:10.1016/j.jnt.2008.07.004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171137 | |
| dc.subject | Number Theory | |
| dc.subject | 14K15 (Primary) 11G10, 14G25, 14L15, 11R45 (Secondary) | |
| dc.title | Prescribing valuations of the order of a point in the reductions of abelian varieties and tori | |
| dc.type | text |