Galois groups and fundamental groups / Tamas Szamuely

Auteur: Szamuely, Tamás (1971-) - AuteurType de document: MonographieCollection: Cambridge studies in advanced mathematics ; 117Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 2009Description: 1 vol. (IX-270 p.) : fig. ; 24 cm ISBN: 9780521888509 ; rel. Note: The book by Szamuely begins with the Galois theory of fields. There is a discussion of topological covering spaces and the related topics of coverings of Riemann surfaces. It is in the fourth chapter that the algebraic étale fundamental group (of algebraic curves) is discussed. The fifth chapter discusses the étale fundamental group of schemes and some of their properties. The last chapter discusses Tannakian categories and the Nori fundamental group scheme. The book is well written and contains much information about the étale fundamental group. There are exercises in every chapter. On the whole, the book is useful for mathematicians and graduate students looking for one place where they can find information about the étale fundamental group and the related Nori fundamental group scheme. (MathSciNet)Résumé: Contents: – Introduction – 1. Galois theory of fields 2. Fundamental groups in topology 3. Riemann surfaces 4. Fundamental groups of algebraic curves 5. Fundamental groups of schemes 6. Tannakian fundamental groups – Bibliography and index.Bibliographie: Bibliogr. p. [261]-267. Index. Sujets MSC: 14E20 Algebraic geometry -- Birational geometry -- Coverings
14H30 Algebraic geometry -- Curves -- Coverings, fundamental group
14F35 Algebraic geometry -- (Co)homology theory -- Homotopy theory; fundamental groups
12F10 Field theory and polynomials -- Field extensions -- Separable extensions, Galois theory
18D10 Category theory; homological algebra -- Categories with structure -- Monoidal categories, symmetric monoidal categories, braided categories
En-ligne: Zentralblatt | MathSciNet
Location Call Number Status Date Due
Salle R 07262-01 / 14 SZA (Browse Shelf) Available

The book by Szamuely begins with the Galois theory of fields. There is a discussion of topological covering spaces and the related topics of coverings of Riemann surfaces. It is in the fourth chapter that the algebraic étale fundamental group (of algebraic curves) is discussed. The fifth chapter discusses the étale fundamental group of schemes and some of their properties. The last chapter discusses Tannakian categories and the Nori fundamental group scheme.
The book is well written and contains much information about the étale fundamental group. There are exercises in every chapter. On the whole, the book is useful for mathematicians and graduate students looking for one place where they can find information about the étale fundamental group and the related Nori fundamental group scheme. (MathSciNet)

Bibliogr. p. [261]-267. Index

Contents: – Introduction – 1. Galois theory of fields 2. Fundamental groups in topology 3. Riemann surfaces 4. Fundamental groups of algebraic curves 5. Fundamental groups of schemes 6. Tannakian fundamental groups – Bibliography and index

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