Galois theories

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Galois theories / Francis Borceux, George Janelidze

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, 2001

形態:

xiv, 341 p. ; 24 cm

シリーズ名:

Cambridge studies in advanced mathematics ; 72 <BA00109761>

著者名:

ISBN:

9780521803090 [0521803098] (: hbk)

書誌ID:

BA50735862

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and indexes

主題:

Galois theory

言語:

英語

目次情報:

Preface

Classical Galois theory / 1：

Algebraic extensions / 1.1：

Separable extensions / 1.2：

Normal extensions / 1.3：

Galois extensions / 1.4：

Galois theory of Grothendieck / 2：

Algebras on a field / 2.1：

Extension of scalars / 2.2：

Split algebras / 2.3：

The Galois equivalence / 2.4：

Infinitary Galois theory / 3：

Finitary Galois subextensions / 3.1：

Infinitary Galois groups / 3.2：

Classical infinitary Galois theory / 3.3：

Profinite topological spaces / 3.4：

Infinitary extension of the Galois theory of Grothendieck / 3.5：

Categorical Galois theory of commutative rings / 4：

Stone duality / 4.1：

Pierce representation of a commutative ring / 4.2：

The adjoint of the 'spectrum' functor / 4.3：

Descent morphisms / 4.4：

Morphisms of Galois descent / 4.5：

Internal presheaves / 4.6：

The Galois theorem for rings / 4.7：

Categorical Galois theorem and factorization systems / 5：

The abstract categorical Galois theorem / 5.1：

Central extensions of groups / 5.2：

Factorization systems / 5.3：

Reflective factorization systems / 5.4：

Semi-exact reflections / 5.5：

Connected components of a space / 5.6：

Connected components of a compact Hausdorff space / 5.7：

The monotone-light factorization / 5.8：

Covering maps / 6：

Categories of abstract families / 6.1：

Some limits in Fam(A) / 6.2：

Involving extensivity / 6.3：

Local connectedness and etale maps / 6.4：

Localization and covering morphisms / 6.5：

Classification of coverings / 6.6：

The Chevalley fundamental group / 6.7：

Path and simply connected spaces / 6.8：

Non-galoisian Galois theory / 7：

Internal presheaves on an internal groupoid / 7.1：

Internal precategories and their presheaves / 7.2：

A factorization system for functors / 7.3：

Generalized descent theory / 7.4：

Generalized Galois theory / 7.5：

Classical Galois theories / 7.6：

Grothendieck toposes / 7.7：

Geometric morphisms / 7.8：

Two dimensional category theory / 7.9：

The Joyal-Tierney theorem / 7.10：

Final remarks / Appendix：

Separable algebras / A.1：

Back to the classical Galois theory / A.2：

Exhibiting some links / A.3：

A short summary of further results and developments / A.4：

Bibliography

Index of symbols

General index

Preface

Classical Galois theory / 1：

Algebraic extensions / 1.1：

Separable extensions / 1.2：

Normal extensions / 1.3：

Galois extensions / 1.4：

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