000 02662nam a22003618i 4500
001 CR9780511471117
003 UkCbUP
005 20200124160238.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090122s1996||||enk o ||1 0|eng|d
020 _a9780511471117 (ebook)
020 _z9780521562805 (hardback)
020 _z9780521065030 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA247
_b.V65 1996
082 0 0 _a512/.3
_220
100 1 _aVölklein, Helmut,
_eauthor.
245 1 0 _aGroups as Galois groups :
_ban introduction /
_cHelmut Völklein.
264 1 _aCambridge :
_bCambridge University Press,
_c1996.
300 _a1 online resource (xvii, 248 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v53
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _a1. 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.
520 _aThis 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.
650 0 _aInverse Galois theory.
776 0 8 _iPrint version:
_z9780521562805
830 0 _aCambridge studies in advanced mathematics ;
_v53.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511471117
999 _c518295
_d518293