Fields of cohomological dimension one versus C_1-fields
| dc.creator | Colliot-Thélène, Jean-Louis | |
| dc.date | 2005-02-09 | |
| dc.date.accessioned | 2026-07-07T05:16:51Z | |
| dc.date.available | 2026-07-07T05:16:51Z | |
| dc.description | Ax gave examples of fields of cohomological dimension 1 which are not C_1-fields. Kato and Kuzumaki asked whether a weak form of the C_1-property holds for all fields of cohomological dimension 1 (existence of solutions in extensions of coprime degree rather than existence of a solution in the ground field). Using work of Merkur'ev and Suslin, and of Rost, D. Madore and I produced examples which show that the answer is in the negative. In the present note, I produce examples which require less work than the original ones. In the original paper, some of the examples were given by forms of degree 3 in 4 variables. Here, for an arbitrary prime p>3, I use forms of degree p in p+1 variables. | |
| dc.description | 5 pages, in English | |
| dc.identifier | https://arxiv.org/abs/math/0502194 | |
| dc.identifier | http://arxiv.org/abs/math/0502194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74139 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 14G05, 12G10, 14C35 ; 14J26, 11E76 | |
| dc.title | Fields of cohomological dimension one versus C_1-fields | |
| dc.type | text |