An Introduction to Galois Cohomology and its ApplicationsThis 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. |
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An Introduction to Galois Cohomology and its Applications Grégory Berhuy Недоступно для просмотра - 2010 |
Часто встречающиеся слова и выражения
1-cocycle abelian action of G acts trivially algebraic closure algebraic group algebraic group-scheme Assume automorphism bijection central simple k-algebra cocycle cohomological invariant cohomology class concludes the proof conjugate connecting map Corollary corresponding defined Definition easy to check element essential dimension etale algebra exact sequence Example exists fc-algebra field field extension K/k finite group first follows G acts G-torsor Galois cohomology Galois descent Galois extension Galois G-algebra Galois group Galois subextension group extension group G group isomorphism group morphism Hence hyperbolic injective involution isomorphism class Lemma Let a G Let F Let G Let K/k matrix Mn(k Moreover natural transformation Notice Ob(C orthogonal particular pointed sets polynomial preimage principal homogeneous space profinite group Proposition prove quadratic form Remark represented ring morphism satisfying Spec(L subgroup subset surjective T-group Theorem topological torsor trace form
Библиографические данные
| Название | An Introduction to Galois Cohomology and its Applications London Mathematical Society Lecture Note Series (Том 377) |
| Автор | Grégory Berhuy |
| Издатель | Cambridge University Press, 2010 |
| ISBN | 1139490885, 9781139490887 |
| Экспорт цитаты | BiBTeX EndNote RefMan |