An introduction to Galois cohomology and its applications

Bibliographic Information

An introduction to Galois cohomology and its applications

Grégory Berhuy

(London Mathematical Society lecture note series, 377)

Cambridge University Press, 2010

  • : pbk

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Note

Includes bibliographical references (p. 310-313) and index

Description and Table of Contents

Description

This is the first elementary introduction to Galois cohomology and its applications. The first part is self-contained and provides the basic results of the theory, including a detailed construction of the Galois cohomology functor, as well as an exposition of the general theory of Galois descent. The author illustrates the theory using the example of the descent problem of conjugacy classes of matrices. The second part of the book gives an insight into how Galois cohomology may be used to solve algebraic problems in several active research topics, such as inverse Galois theory, rationality questions or the essential dimension of algebraic groups. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.

Table of Contents

  • Foreword Jean-Pierre Tignol
  • Introduction
  • Part I. An Introduction to Galois Cohomology: 1. Infinite Galois theory
  • 2. Cohomology of profinite groups
  • 3. Galois cohomology
  • 4. Galois cohomology of quadratic forms
  • 5. Etale and Galois algebras
  • 6. Groups extensions and Galois embedding problems
  • Part II. Applications: 7. Galois embedding problems and the trace form
  • 8. Galois cohomology of central simple algebras
  • 9. Digression: a geometric interpretation of H1 (-, G)
  • 10. Galois cohomology and Noether's problem
  • 11. The rationality problem for adjoint algebraic groups
  • 12. Essential dimension of functors
  • References
  • Index.

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Details
  • NCID
    BB0323134X
  • ISBN
    • 9780521738668
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge [England] ; Tokyo
  • Pages/Volumes
    xi, 315 p.
  • Size
    23 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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