On the Manin-Mumford conjecture for abelian varieties with a prime of supersingular reduction
| dc.creator | Ito, Tetsushi | |
| dc.date | 2004-11-12 | |
| dc.date.accessioned | 2026-07-07T05:14:17Z | |
| dc.date.available | 2026-07-07T05:14:17Z | |
| dc.description | We give a short proof of the "prime-to-$p$ version" of the Manin-Mumford conjecture for an abelian variety over a number field, when it has supersingular reduction at a prime dividing $p$, by combining the methods of Bogomolov, Hrushovski, and Pink-Roessler. Our proof here is quite simple and short, and neither $p$-adic Hodge theory nor model theory is used. The observation is that a power of a lift of the Frobenius element at a supersingular prime acts on the prime-to-$p$ torsion points via nontrivial homothety. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411291 | |
| dc.identifier | http://arxiv.org/abs/math/0411291 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73216 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary: 14K12; Secondary: 11G10, 14G15 | |
| dc.title | On the Manin-Mumford conjecture for abelian varieties with a prime of supersingular reduction | |
| dc.type | text |