An Introduction to Galois Cohomology and Its Applications

An Introduction to Galois Cohomology and Its Applications

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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.show more

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Review quote

'... 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 MATHshow more

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.show more

About Gregory Berhuy

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