紹介
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.
目次
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.
