Asymptotic Brauer p-dimension

Adam Chapman, Kelly McKinnie

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We define and compute the asymptotic Brauer p-dimension of a field F, denoted ABrdp(F), in cases where F is a rational function field or Laurent series field. ABrdp(F) is defined like the Brauer p-dimension except it considers finite sets of Brauer classes instead of single classes. Our main result shows that for fields F01,…, αn) and F0((α1))… ((αn)) where F0 is a perfect field of characteristic p > 0 when n ≥ 2 the asymptotic Brauer p- dimension is n. We also show that it is n − 1 when F = F0((α1))… ((αn)) and F0 is algebraically closed of characteristic not p.

Original languageEnglish
Title of host publicationAlgebra and Coding Theory- Virtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Applications VII, 2021 and Virtual Conference on Quadratic Forms, Rings and Codes, 2021
EditorsA. Leroy, S.K. Jain
PublisherAmerican Mathematical Society
Pages57-66
Number of pages10
ISBN (Print)9781470468590
DOIs
StatePublished - 2023
EventVirtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Application VII, NCRA 2021, and Virtual Conference on Quadratic forms, rings and codes, QFRC 2021 - Virtual, Online
Duration: Jul 8 2021Jul 8 2021

Publication series

NameContemporary Mathematics
Volume785
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceVirtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Application VII, NCRA 2021, and Virtual Conference on Quadratic forms, rings and codes, QFRC 2021
CityVirtual, Online
Period07/8/2107/8/21

Keywords

  • cyclic algebras
  • Division algebras
  • fields of positive characteristic
  • linkage
  • valuation theory

Fingerprint

Dive into the research topics of 'Asymptotic Brauer p-dimension'. Together they form a unique fingerprint.

Cite this