Value Functions on Simple Algebras, and Associated Graded Rings

  • Jean-Pierre Tignol
  • Adrian R. Wadsworth

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 1-32
  3. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 33-80
  4. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 81-133
  5. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 135-192
  6. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 193-237
  7. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 239-296
  8. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 297-376
  9. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 377-454
  10. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 455-490
  11. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 491-534
  12. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 535-559
  13. Jean-Pierre Tignol, Adrian R. Wadsworth
    Pages 561-584
  14. Back Matter
    Pages 585-643

About this book

Introduction

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the Tannaka-Artin problem.

This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased.

The intended audience consists of graduate students and research mathematicians.

Keywords

Associated Graded Algebra Brauer Group Division Algebra Ramification Valuation

Authors and affiliations

  • Jean-Pierre Tignol
    • 1
  • Adrian R. Wadsworth
    • 2
  1. 1.ICTEAM Institute, Université Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of MathematicsUniversity of California San DiegoLa JollaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16360-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16359-8
  • Online ISBN 978-3-319-16360-4
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book