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An Introduction to Galois Cohomology and its Applications Gregory Berhuy (Universite Joseph Fourier, Grenoble)

An Introduction to Galois Cohomology and its Applications By Gregory Berhuy (Universite Joseph Fourier, Grenoble)

An Introduction to Galois Cohomology and its Applications by Gregory Berhuy (Universite Joseph Fourier, Grenoble)


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Summary

This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.

An Introduction to Galois Cohomology and its Applications Summary

An Introduction to Galois Cohomology and its Applications by Gregory Berhuy (Universite Joseph Fourier, Grenoble)

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.

An Introduction to Galois Cohomology and its Applications Reviews

'... beautifully covers several active areas in contemporary Galois theory which are presently not treated in other standard textbooks on Galois cohomology. The exposition is detailed and leisurely, and is therefore suited also for advanced graduate students ...' Mathematical Reviews
'This book is a very welcome addition to the literature for people doing research in Galois cohomology or using it as a tool in their research or in lecture courses.' Zentralblatt MATH

About Gregory Berhuy (Universite Joseph Fourier, Grenoble)

Gregory Berhuy is a Professor at the Universite Joseph Fourier, Grenoble, France.

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.

Additional information

NLS9780521738668
9780521738668
0521738660
An Introduction to Galois Cohomology and its Applications by Gregory Berhuy (Universite Joseph Fourier, Grenoble)
New
Paperback
Cambridge University Press
2010-09-09
328
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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