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Brauer Type Embedding Problems
Arne Ledet, Texas Tech University, Lubbock, TX
A co-publication of the AMS and Fields Institute.
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Fields Institute Monographs
2005; 171 pp; hardcover
Volume: 21
ISBN-10: 0-8218-3726-5
ISBN-13: 978-0-8218-3726-9
List Price: US$58
Member Price: US$46.40
Order Code: FIM/21
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This monograph is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. The advantage of considering Brauer type embedding problems is their comparatively simple condition for solvability in the form of an obstruction in the Brauer group of the ground field.

The book presupposes knowledge of classical Galois theory and the attendant algebra. Before considering questions of reducing the embedding problems and reformulating the solvability criteria, the author provides the necessary theory of Brauer groups, group cohomology and quadratic forms. The book will be suitable for students seeking an introduction to embedding problems and inverse Galois theory. It will also be a useful reference for researchers in the field.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in embedding problems and inverse Galois theory.

Reviews

"But if you wish to learn about Brauer type embedding problems, and if you want to see a crystal-clear and beautiful picture with a number of delightful examples, with a friendly and witty guide, you cannot do better than to read this fine book by Arne Ledet."

-- CMS Notes

"Throughout the monograph, presentations are very crisp and clear. Each chapter is supplemented by a large collection of exercises. The monograph may be used as a textbook for an advanced algebra course."

-- Zentralblatt Math

Table of Contents

  • Galois theory
  • Inverse Galois theory and embedding problems
  • Brauer groups
  • Group cohomology
  • Quadratic forms
  • Decomposing the obstruction
  • Quadratic forms and embedding problems
  • Reducing the embedding problem
  • Pro-finite Galois theory
  • Bibliography
  • Index
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