Orbits of automorphism groups of fields
| dc.creator | Kedlaya, Kiran S. | |
| dc.creator | Poonen, Bjorn | |
| dc.date | 2004-07-27 | |
| dc.date | 2005-06-28 | |
| dc.date.accessioned | 2026-07-07T05:10:45Z | |
| dc.date.available | 2026-07-07T05:10:45Z | |
| dc.description | We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has relatively few orbits? We prove that any field which has only finitely many orbits under its automorphism group is finite. We extend the techniques of that proof to approach a broader conjecture, which asks whether the automorphism group of one field over a subfield can have only finitely many orbits on the complement of the subfield. Finally, we apply similar methods to analyze the field of Mal'cev-Neumann "generalized power series" over a base field; these form near-counterexamples to our conjecture when the base field has characteristic zero, but often fall surprisingly far short in positive characteristic. | |
| dc.description | 15 pages; v2: refereed version | |
| dc.identifier | https://arxiv.org/abs/math/0407473 | |
| dc.identifier | http://arxiv.org/abs/math/0407473 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72028 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Number Theory | |
| dc.subject | 12F10 (Primary) 12J25 (Secondary) | |
| dc.title | Orbits of automorphism groups of fields | |
| dc.type | text |