An Introduction to Galois Cohomology and its Applications
An Introduction to Galois Cohomology and its Applications
$89.99
USDThis 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
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
Product details
October 2010Paperback
9780521738668
328 pages
228 × 152 × 17 mm
0.47kg
65 exercises
Available
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.
