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 algeb...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1996
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
53 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xvii, 248 Seiten) |
| ISBN: | 9780511471117 |
| DOI: | 10.1017/CBO9780511471117 |
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| 100 | 1 | |a Völklein, Helmut |d 1957- |e Verfasser |0 (DE-588)11016055X |4 aut | |
| 245 | 1 | 0 | |a Groups as Galois groups |b an introduction |c Helmut Völklein |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 53 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |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 | ||
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Datensatz im Suchindex
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| author | Völklein, Helmut 1957- |
| author_GND | (DE-588)11016055X |
| author_facet | Völklein, Helmut 1957- |
| author_role | aut |
| author_sort | Völklein, Helmut 1957- |
| author_variant | h v hv |
| building | Verbundindex |
| bvnumber | BV043942103 |
| classification_rvk | SK 230 SK 200 |
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| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511471117 (OCoLC)849876680 (DE-599)BVBBV043942103 |
| dewey-full | 512/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.3 |
| dewey-search | 512/.3 |
| dewey-sort | 3512 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511471117 |
| format | Electronic eBook |
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| id | DE-604.BV043942103 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511471117 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351073 |
| oclc_num | 849876680 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| physical | 1 Online-Ressource (xvii, 248 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Völklein, Helmut 1957- Verfasser (DE-588)11016055X aut Groups as Galois groups an introduction Helmut Völklein Cambridge Cambridge University Press 1996 1 Online-Ressource (xvii, 248 Seiten) txt rdacontent c rdamedia cr rdacarrier 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 Inverse Galois theory Galois-Gruppe (DE-588)4155897-2 gnd rswk-swf Galois-Gruppe (DE-588)4155897-2 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-56280-5 Erscheint auch als Druck-Ausgabe 978-0-521-06503-0 Cambridge studies in advanced mathematics 53 (DE-604)BV044781283 53 https://doi.org/10.1017/CBO9780511471117 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Völklein, Helmut 1957- Groups as Galois groups an introduction Cambridge studies in advanced mathematics 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 Inverse Galois theory Galois-Gruppe (DE-588)4155897-2 gnd |
| subject_GND | (DE-588)4155897-2 |
| title | Groups as Galois groups an introduction |
| title_auth | Groups as Galois groups an introduction |
| title_exact_search | Groups as Galois groups an introduction |
| title_full | Groups as Galois groups an introduction Helmut Völklein |
| title_fullStr | Groups as Galois groups an introduction Helmut Völklein |
| title_full_unstemmed | Groups as Galois groups an introduction Helmut Völklein |
| title_short | Groups as Galois groups |
| title_sort | groups as galois groups an introduction |
| title_sub | an introduction |
| topic | Inverse Galois theory Galois-Gruppe (DE-588)4155897-2 gnd |
| topic_facet | Inverse Galois theory Galois-Gruppe |
| url | https://doi.org/10.1017/CBO9780511471117 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT volkleinhelmut groupsasgaloisgroupsanintroduction |