Rational points in periodic analytic sets and the Manin-Mumford conjecture
| dc.creator | Pila, Jonathan | |
| dc.creator | Zannier, Umberto | |
| dc.date | 2008-02-27 | |
| dc.date.accessioned | 2026-07-07T09:23:35Z | |
| dc.date.available | 2026-07-07T09:23:35Z | |
| dc.description | We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to view torsion points as rational points on a complex torus and then compare (i) upper bounds for the number of rational points on a transcendental analytic variety (Bombieri-Pila-Wilkie) and (ii) lower bounds for the degree of a torsion point (Masser), after taking conjugates. In order to be able to deal with (i), we discuss (Thm. 2.1) the semi-algebraic curves contained in an analytic variety supposed invariant for translations by a full lattice, which is a topic with some independent motivation. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0802.4016 | |
| dc.identifier | http://arxiv.org/abs/0802.4016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155782 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Rational points in periodic analytic sets and the Manin-Mumford conjecture | |
| dc.type | text |