Connected Components of Hurwitz Schemes and Malle's Conjecture
| dc.creator | Turkelli, Seyfi | |
| dc.date | 2008-09-05 | |
| dc.date | 2008-09-16 | |
| dc.date.accessioned | 2026-07-07T10:02:42Z | |
| dc.date.available | 2026-07-07T10:02:42Z | |
| dc.description | Let Z(X) be the number of degree-d extensions of F_q(t) with bounded discriminant and some specified Galois group. The problem of computing Z(X) can be related to a problem of counting F_q-rational points on certain Hurwitz spaces. Ellenberg and Venkatesh used this idea to develop a heuristic for the asymptotic behavior of Z'(X), the number of -geometrically connected- extensions, and showed that this agrees with the conjectures of Malle for function fields. We extend Ellenberg-Venkatesh's argument to handle the more complicated case of covers of P^1 which may not be geometrically connected, and show thatthe resulting heuristic suggests a natural modification to Malle's conjecture which avoids the counterexamples, due to Klüners, to the original conjecture. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0809.0951 | |
| dc.identifier | http://arxiv.org/abs/0809.0951 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169068 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Connected Components of Hurwitz Schemes and Malle's Conjecture | |
| dc.type | text |