On elementary equivalence, isomorphism and isogeny of arithmetic function fields
| dc.creator | Clark, Pete L. | |
| dc.date | 2004-06-08 | |
| dc.date.accessioned | 2026-07-07T05:08:58Z | |
| dc.date.available | 2026-07-07T05:08:58Z | |
| dc.description | Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and of quadric surfaces. These results are applied to deduce new instances of "elementary equivalence implies isomorphism": for all genus zero curves over a number field, and for certain genus one curves over a number field, including some which are not elliptic curves. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406133 | |
| dc.identifier | http://arxiv.org/abs/math/0406133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71471 | |
| dc.subject | Logic | |
| dc.subject | Number Theory | |
| dc.title | On elementary equivalence, isomorphism and isogeny of arithmetic function fields | |
| dc.type | text |