Integrality at a prime for global fields and the perfect closure of global fields of characteristic p>2
| dc.creator | Eisentraeger, Kirsten | |
| dc.date | 2003-10-15 | |
| dc.date | 2006-09-20 | |
| dc.date.accessioned | 2026-07-07T06:35:45Z | |
| dc.date.available | 2026-07-07T06:35:45Z | |
| dc.description | Let k be a global field and \pp any nonarchimedean prime of k. We give a new and uniform proof of the well known fact that the set of all elements of k which are integral at \pp is diophantine over k. Let k^{perf} be the perfect closure of a global field of characteristic p>2. We also prove that the set of all elements of k^{perf} which are integral at some prime \qq of k^{perf} is diophantine over k^{perf}, and this is the first such result for a field which is not finitely generated over its constant field. This is related to Hilbert's Tenth Problem because for global fields k of positive characteristic, giving a diophantine definition of the set of elements that are integral at a prime is one of two steps needed to prove that Hilbert's Tenth Problem for k is undecidable. | |
| dc.description | 10 pages; minor revisions made | |
| dc.identifier | https://arxiv.org/abs/math/0310224 | |
| dc.identifier | http://arxiv.org/abs/math/0310224 | |
| dc.identifier | J. Number Theory 114 (1) (2005), 170-181 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99889 | |
| dc.subject | Number Theory | |
| dc.subject | 11U05 (Primary); 03B25 (Secondary) | |
| dc.title | Integrality at a prime for global fields and the perfect closure of global fields of characteristic p>2 | |
| dc.type | text |