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170324  eng 
020 


a 9780511471117

050 

4 
a QA247

100 
1 

a Völklein, Helmut

245 
0 
0 
a Groups as Galois groups
b an introduction
c Helmut Völklein

260 


a Cambridge
b Cambridge University Press
c 1996

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

041 
0 
7 
a eng
2 ISO 6392

989 


b CBO
a Cambridge Books Online

490 
0 

a Cambridge studies in advanced mathematics

028 
5 
0 
a 10.1017/CBO9780511471117

856 
4 
0 
u https://doi.org/10.1017/CBO9780511471117
x Verlag
3 Volltext

082 
0 

a 512.3

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
