Canonical Invariants for Corresponding Residue Systems in P-Adic Fields

Let F be a finite extension of $\doubq\sb{p}$. Let L/F be a normal, totally ramified extension of degree $p\sp{2n}$ with ${\cal B}$ the maximal ideal of ${\cal D}\sb{\rm L}$. Suppose the Hilbert sequence for L/F has a unique breakpoint at $t$. That is, if ${\cal G}$ = Gal(L/F), then its Hilbert sequence is ${\cal G}$ = ${\cal G}\sb0$ = ${\cal G}\sb1$ = $\cdots$ = ${\cal G}\sb{t}\ne{\cal G}\sb{t+1}$ = $\{1\}$. For a subextension K/F of degree $p\sp{n}$ with G = Gal(K/F), we define $\Theta\sbsp{\rm K}{\rm L}$: G $\mapsto$ ${\cal B}\sp{tp\sp{\rm n}}/{\cal B}\sp{tp{\sp\rm n}+1}$ by σ $\mapsto$ {σπ-π}\over{π} + ${\cal B}\sp{tp\sp{\rm n}+1}$, where π is a uniformizer for K/F. If K$\sp\prime$/F is another subextension of degree $p\sp{n}$ with G$\sp\prime$ = Gal(K$\sp\prime$/F), we similarly define $\Theta\sbsp{\rm K\sp\prime}{\rm L}$: G$\sp\prime$ $\to$ ${\cal B}\sp{tp\sp{\rm n}}/{\cal B}\sp{tp\sp{\rm n}+1}.$

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Benson, Steven Rex

Contributors dc:contributor

• McCulloh, Leon R.,

• Mathematics

Identifier

(UMI)AAI8908621

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71269