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An Introduction to Galois Cohomology and its Applications

$91.99

Part of London Mathematical Society Lecture Note Series

Jean-Pierre Tignol
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  • Date Published: October 2010
  • availability: In stock
  • format: Paperback
  • isbn: 9780521738668

$91.99
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  • This book 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 whole theory is motivated and illustrated using the example of the descent problem of conjugacy classes of matrices. The second part of the book gives an insight of how Galois cohomology may be useful to solve some algebraic problems in several active research topics, such as inverse Galois theory, rationality questions or essential dimension of algebraic groups. The author assumes only a minimal background in algebra (Galois theory, tensor products of vectors spaces and algebras).

    • Presents the basic theory using detailed proofs
    • Provides a wide range of applications of Galois cohomology
    • Only prerequisites are Galois theory, tensor products of vector spaces and algebras
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    Reviews & endorsements

    "It beautifully covers several active areas in contemporary Galois theory which are not presently treated in other standard textbooks on Galois cohomology."
    Ido Efrat, Mathematical Reviews

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    Product details

    • Date Published: October 2010
    • format: Paperback
    • isbn: 9780521738668
    • length: 328 pages
    • dimensions: 228 x 152 x 17 mm
    • weight: 0.47kg
    • contains: 65 exercises
    • availability: In stock
  • 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.

  • Author

    Grégory Berhuy, Université Joseph Fourier, Grenoble
    Grégory Berhuy is a Professor at the Université Joseph Fourier, Grenoble, France.

    Contributors

    Jean-Pierre Tignol

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