On the Andre-Oort conjecture for Hilbert modular surfaces
| dc.creator | Edixhoven, Bas | |
| dc.date | 1999-11-15 | |
| dc.date.accessioned | 2026-07-07T05:32:02Z | |
| dc.date.available | 2026-07-07T05:32:02Z | |
| dc.description | We prove, assuming the generalized Riemann hypothesis, the Andre-Oort conjecture for Hilbert modular surfaces. More precisely, let K be a real quadratic field and let S be the coarse moduli space of complex abelian surfaces with multiplications by the ring of integers of K. Let C be an irreducible closed curve in S, and suppose that C contains infinitely many complex multiplication points. Then we prove, assuming GRH, that C is of Hodge type, meaning, in this case, that it parametrizes abelian varieties with more endomorphisms. Also, if we assume that C has infinitely many CM points that correspond to abelian surfaces that lie in one isogeny class, we prove that C is of Hodge type without assuming GRH. This last result is motivated by applications by Wolfart, Cohen and Wustholz. | |
| dc.identifier | https://arxiv.org/abs/math/9911272 | |
| dc.identifier | http://arxiv.org/abs/math/9911272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79517 | |
| dc.subject | Number Theory | |
| dc.title | On the Andre-Oort conjecture for Hilbert modular surfaces | |
| dc.type | text |