Enumeration of Isomorphism Classes of Extensions of p-adic Fields
| dc.creator | Hou, Xiang-dong | |
| dc.creator | Keating, Kevin | |
| dc.date | 2001-10-04 | |
| dc.date.accessioned | 2026-07-07T04:43:40Z | |
| dc.date.available | 2026-07-07T04:43:40Z | |
| dc.description | Let $Ω$ be an algebraic closure of ${\mathbb Q}_p$ and let $F$ be a finite extension of ${\mathbb Q}_p$ contained in $Ω$. Given positive integers $f$ and $e$, the number of extensions $K/F$ contained in $Ω$ with residue degree $f$ and ramification index $e$ was computed by Krasner. This paper is concerned with the number ${\mathfrak I}(F,f,e)$ of $F$-isomorphism classes of such extensions. We determine ${\mathfrak I}(F,f,e)$ completely when $p^2\nmid e$ and get partial results when $p^2\parallel e$. When $s$ is large, ${\mathfrak I}({\mathbb Q}_p,f,e)$ is equal to the number of isomorphism classes of finite commutative chain rings with residue field ${\mathbb F}_{p^f}$, ramification index $e$, and length $s$. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0110055 | |
| dc.identifier | http://arxiv.org/abs/math/0110055 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62326 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11S15 | |
| dc.title | Enumeration of Isomorphism Classes of Extensions of p-adic Fields | |
| dc.type | text |