Finite automata and algebraic extensions of function fields
| dc.creator | Kedlaya, Kiran S. | |
| dc.date | 2004-10-17 | |
| dc.date | 2005-05-04 | |
| dc.date.accessioned | 2026-07-07T05:13:20Z | |
| dc.date.available | 2026-07-07T05:13:20Z | |
| dc.description | We give an automata-theoretic description of the algebraic closure of the rational function field F_q(t) over a finite field, generalizing a result of Christol. The description takes place within the Hahn-Mal'cev-Neumann field of "generalized power series" over F_q. Our approach includes a characterization of well-ordered sets of rational numbers whose base p expansions are generated by a finite automaton, as well as some techniques for computing in the algebraic closure; these include an adaptation to positive characteristic of Newton's algorithm for finding local expansions of plane curves. We also conjecture a generalization of our results to several variables. | |
| dc.description | 40 pages; expanded version of math.AC/0110089; v2: refereed version, includes minor edits | |
| dc.identifier | https://arxiv.org/abs/math/0410375 | |
| dc.identifier | http://arxiv.org/abs/math/0410375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72910 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Number Theory | |
| dc.subject | 13P05 | |
| dc.title | Finite automata and algebraic extensions of function fields | |
| dc.type | text |