An Introduction to Galois Cohomology and its Applications

Erscheinungsjahr 2010
ISBN: 978-0-521-73866-8
Verlag: Cambridge University Press

Buch, Englisch, Band 377, 328 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 477 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Berhuy, Grégory

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Berhuy, Grégory
Grégory Berhuy is a Professor at the Université Joseph Fourier, Grenoble, France.

Grégory Berhuy is a Professor at the Université Joseph Fourier, Grenoble, France.