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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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