Groups as Galois groups an introduction

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algeb...

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Bibliographic Details
Main Author: Völklein, Helmut
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 1996
Series:Cambridge studies in advanced mathematics
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
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245 0 0 |a Groups as Galois groups  |b an introduction  |c Helmut Völklein 
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300 |a xvii, 248 pages  |b digital 
505 0 |a 1. Hilbert's Irreducibility Theorem -- 2. Finite Galois Extensions of C(x) -- 3. Descent of Base Field and the Rigidity Criterion -- 4. Covering Spaces and the Fundamental Group -- 5. Riemann Surfaces and Their Function Fields -- 6. The Analytic Version of Riemann's Existence Theorem -- 7. The Descent from C to [actual symbol not reproducible] -- 8. Embedding Problems -- 9. Braiding Action and Weak Rigidity -- 10. Moduli Spaces for Covers of the Riemann Sphere -- 11. Patching over Complete Valued Fields 
653 |a Inverse Galois theory 
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520 |a This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field