The tame-wild principle for discriminant relations for number fields

John Jones, David P. Roberts

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Consider tuples (K1,..., Kr)of separable algebras over a common local or global number field F, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki =F. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.

Original languageEnglish (US)
Pages (from-to)609-645
Number of pages37
JournalAlgebra and Number Theory
Volume8
Issue number3
DOIs
StatePublished - 2014

Fingerprint

Divisibility
Ramification
Resolvent
Discriminant
Number field
Simple group
Continue
Algebra

Keywords

  • Discriminant
  • Number field
  • Ramification

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

The tame-wild principle for discriminant relations for number fields. / Jones, John; Roberts, David P.

In: Algebra and Number Theory, Vol. 8, No. 3, 2014, p. 609-645.

Research output: Contribution to journalArticle

@article{48af6b681ecb4e06ac07dd215b325e8d,
title = "The tame-wild principle for discriminant relations for number fields",
abstract = "Consider tuples (K1,..., Kr)of separable algebras over a common local or global number field F, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki =F. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.",
keywords = "Discriminant, Number field, Ramification",
author = "John Jones and Roberts, {David P.}",
year = "2014",
doi = "10.2140/ant.2014.8.609",
language = "English (US)",
volume = "8",
pages = "609--645",
journal = "Algebra and Number Theory",
issn = "1937-0652",
publisher = "Mathematical Sciences Publishers",
number = "3",

}

TY - JOUR

T1 - The tame-wild principle for discriminant relations for number fields

AU - Jones, John

AU - Roberts, David P.

PY - 2014

Y1 - 2014

N2 - Consider tuples (K1,..., Kr)of separable algebras over a common local or global number field F, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki =F. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.

AB - Consider tuples (K1,..., Kr)of separable algebras over a common local or global number field F, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki =F. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.

KW - Discriminant

KW - Number field

KW - Ramification

UR - http://www.scopus.com/inward/record.url?scp=84902979278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902979278&partnerID=8YFLogxK

U2 - 10.2140/ant.2014.8.609

DO - 10.2140/ant.2014.8.609

M3 - Article

AN - SCOPUS:84902979278

VL - 8

SP - 609

EP - 645

JO - Algebra and Number Theory

JF - Algebra and Number Theory

SN - 1937-0652

IS - 3

ER -