Vari'et'es presque rationnelles, leurs points rationnels et leurs d'eg'en'erescences
| dc.creator | Colliot-Thélène, J-L. | |
| dc.date | 2008-09-08 | |
| dc.date.accessioned | 2026-07-07T10:01:27Z | |
| dc.date.available | 2026-07-07T10:01:27Z | |
| dc.description | This survey, which contains very few proofs, addresses the general question: Over a given type of field, is there a natural class of varieties which automatically have a rational point? Fields under consideration here include: finite fields, p-adic fields, function fields in one or two variables over an algebraically closed field. Classical answers are given by the Chevalley-Warning theorem and by Tsen's theorem. More general answers were provided by a theorem of Graber, Harris and Starr and by a theorem of Esnault. The latter results apply to rationally connected varieties. We discuss these varieties from various angles : weak approximation, R-equivalence, Chow group of zero-cycles. Ongoing work on `rationally simply connected' varieties over function fields in two variables is also mentioned. A common thread in this report is the study of the special fibre of a scheme over a discrete valuation ring: if the generic fibre has a simple geometry, what does it imply for the special fibre? | |
| dc.description | Lecture notes for a CIME summer school (Cetraro, September 2007), 56 pages, in French | |
| dc.identifier | https://arxiv.org/abs/0809.1386 | |
| dc.identifier | http://arxiv.org/abs/0809.1386 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168633 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G05, 14D06, 14M20, 14G99, 14E99 | |
| dc.title | Vari'et'es presque rationnelles, leurs points rationnels et leurs d'eg'en'erescences | |
| dc.type | text |