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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.

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Book Details

ISBN: 9780521065030
ISBN-10: 0521065038
Format: Paperback
(228mm x 152mm x 15mm)
Pages: 268
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 12-Jun-2008
Country of Publication: United Kingdom

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Books By Author Helmut Volklein

Groups as Galois Groups by Helmut Volklein

Groups as Galois Groups

Hardback, August 1996
$243.00