Lifting results for rational points on Hurwitz moduli spaces
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Théorie des Nombres et Algorithmique Arithmétique [A2X] | |
| dc.contributor.author | CADORET, Anna | |
| dc.date.issued | 2008 | |
| dc.identifier.issn | 0021-2172 | |
| dc.description.abstractEn | Hurwitz moduli spaces for G-covers of the pro jective line have two classical variants whether G- covers are considered modulo the action of PGL2 on the base or not. A central result of this paper is that, given an integer r ≥ 3 there exists a bound d(r) ≥ 1 depending only on r such that any rational point p rd of a reduced (i.e. modulo PGL2 ) Hurwitz space can be lifted to a rational point p on the non reduced Hurwitz space with [κ(p) : κ(prd )] ≤ d(r). This result can also be generalized to infinite towers of Hurwitz spaces. Introducing a new Galois invariant for G-covers, which we call the base invariant, we improve this result for G-covers with a non trivial base invariant. For the sublocus corresponding to such G-covers the bound d(r) can be chosen depending only on the base invariant (no longer on r) and ≤ 6. When r = 4, our method can still be refined to provide effective criteria to lift k-rational points from reduced to non reduced Hurwitz spaces. This, in particular, leads to a rigidity criterion, a genus 0 method and, what we call an expansion method to realize finite groups as regular Galois groups over Q. Some specific examples are given. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Lifting results for rational points on Hurwitz moduli spaces | |
| dc.type | Article de revue | |
| bordeaux.journal | Israel Journal of Mathematics | |
| bordeaux.page | 19-61 | |
| bordeaux.volume | 164 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00355695 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00355695v1 | |
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