Galois groups and fundamental groups / Tamas Szamuely
Type de document : MonographieCollection : Cambridge studies in advanced mathematics, 117Langue : anglais.Pays: Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 2009Description : 1 vol. (IX-270 p.) : fig. ; 24 cmISBN: 9780521888509.ISSN: 0950-6330.Bibliographie : Bibliogr. p. [261]-267. Index.Sujet MSC : 14E20, Algebraic geometry - Birational geometry, Coverings14H30, Curves in algebraic geometry, Coverings of curves, fundamental group
14F35, (Co)homology theory in algebraic geometry, Homotopy theory and fundamental groups
12F10, Field theory and polynomials - Field extensions, Separable extensions, Galois theory
18M05, Monoidal categories and operads, Monoidal categories, symmetric monoidal categoriesEn-ligne : Zentralblatt | MathSciNet
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Monographie
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CMI Salle 1 | 14 SZA (Browse shelf(Opens below)) | Available | 07262-01 |
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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