Curves that change genus can have arbitrarily many rational points
| dc.creator | Voloch, Jose' Felipe | |
| dc.date | 1995-06-06 | |
| dc.date.accessioned | 2026-07-07T09:06:33Z | |
| dc.date.available | 2026-07-07T09:06:33Z | |
| dc.description | A singular curve over a non-perfect field K may not have a smooth model over K. Those are said to "change genus". If K is a global field of positive characteristic and C/K a curve that change genus, then C(K) is known to be finite. The purpose of this note is to give examples of curves with fixed relative genus, defined over K for which #C(K) is arbitrarily large. The motivation for considering this problem comes from the work of Caporaso et al. [CHM], where they show that a conjecture of Lang implies that, for a number field K, #C(K) can be bounded in terms of g and K only for all curves C/K of genus g > 1. | |
| dc.description | plain TeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9506009 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9506009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150050 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G25 (Primary) 11G30 (Secondary) | |
| dc.title | Curves that change genus can have arbitrarily many rational points | |
| dc.type | text |