Enumeration of Isomorphism Classes of Extensions of p-adic Fields

Details Enumeration of Isomorphism Classes of Extensions of p-adic Fields Enumeration of Isomorphism Classes of Extensions of p-adic Fields

2001-10-04

arxiv.org/abs/math/0110055v1

Mathematics

Number Theory

39 pages

Scientific paper

Let $\Omega$ be an algebraic closure of ${\mathbb Q}_p$ and let $F$ be a finite extension of ${\mathbb Q}_p$ contained in $\Omega$. Given positive integers $f$ and $e$, the number of extensions $K/F$ contained in $\Omega$ 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 $s$.

Affiliated with

Also associated with

No associations

Rating

Enumeration of Isomorphism Classes of Extensions of p-adic Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Enumeration of Isomorphism Classes of Extensions of p-adic Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enumeration of Isomorphism Classes of Extensions of p-adic Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-417300