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Groups as Galois groups = an introdu...

Volklein, Helmut.

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Groups as Galois groups = an introduction /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Groups as Galois groups/ Helmut Volklein.
其他題名:	an introduction /
作者:	Volklein, Helmut.
出版者:	Cambridge :Cambridge University Press, : 1996.,
面頁冊數:	xvii, 248 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Inverse Galois theory. -
電子資源:	https://doi.org/10.1017/CBO9780511471117
ISBN:	9780511471117

Groups as Galois groups = an introduction /
Volklein, Helmut.

Groups as Galois groupsan introduction /[electronic resource] :Helmut Volklein. - Cambridge :Cambridge University Press,1996. - xvii, 248 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;53. - Cambridge studies in advanced mathematics ;53..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9780511471117Subjects--Topical Terms:

708423
Inverse Galois theory.

LC Class. No.: QA247 / .V65 1996

Dewey Class. No.: 512.3

Groups as Galois groups = an introduction /
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300 $a xvii, 248 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 53
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
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.
650 0 $a Inverse Galois theory. $3 708423
830 0 $a Cambridge studies in advanced mathematics ; $v 53. $3 3470643
856 4 0 $u https://doi.org/10.1017/CBO9780511471117