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 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 basi…
Read More ↓Title Statements
- Full title :Groups as Galois groups : an introduction / Helmut Völklein (University of Florida und Universität Erlangen).
Summary
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.
Read More ↓Edition Statements
- Publication Date:2008
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:New York
- Language:eng
- Publication Date:2008
Notes
MSC 11R32 ; 11S20 ; 12F10 ; 12F12 ; 13B05.
The Physical Object
- Description:XVII, 248 p.; : 24 cm
Edition Identifiers
- ISBN:9780521562805, 0521562805, 9780521065030, 0521065038
- oclc:on1322909924
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