Special points on products of modular curves
| dc.creator | Edixhoven, Bas | |
| dc.date | 2003-02-12 | |
| dc.date | 2004-10-26 | |
| dc.date.accessioned | 2026-07-07T08:37:48Z | |
| dc.date.available | 2026-07-07T08:37:48Z | |
| dc.description | We prove the Andre-Oort conjecture on special points of Shimura varieties for arbitrary products of modular curves, assuming the Generalized Riemann Hypothesis. More explicitly, this means the following. Let n be a positive integer, and let S be a subset of C^n (with C the complex numbers) consisting of points all of whose coordinates are j-invariants of elliptic curves with complex multiplications. Then we prove (under GRH) that the irreducible components of the Zariski closure of S are ``special subvarieties'', i.e., determined by isogeny conditions on coordinates and pairs of coordinates. A weaker variant is proved unconditionally. | |
| dc.description | 21 pages, referee's remarks have been taken into account, some references updated, to appear in Duke Mathematical Journal | |
| dc.identifier | https://arxiv.org/abs/math/0302138 | |
| dc.identifier | http://arxiv.org/abs/math/0302138 | |
| dc.identifier | Duke Math. J. 126 (2005), no. 2, 325--348. | |
| dc.identifier | doi:10.1215/S0012-7094-04-12624-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140531 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G35, 14K22, 11G15 | |
| dc.title | Special points on products of modular curves | |
| dc.type | text |