An Introduction to Galois Cohomology and its Applications

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Enabling JavaScript in your browser will allow you to experience all the features of our site. Learn how to enable JavaScript on your browser. This book is the first elementary introduction to Galois cohomology and its applications.

An 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.

Introduction to Galois Theory

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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.


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