Introduction to Cyclotomic Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1982
|
| Schriftenreihe: | Graduate Texts in Mathematics
83 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2 |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781468401332 9781468401356 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-0133-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421007 | ||
| 003 | DE-604 | ||
| 005 | 20160714 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1982 |||| o||u| ||||||eng d | ||
| 020 | |a 9781468401332 |c Online |9 978-1-4684-0133-2 | ||
| 020 | |a 9781468401356 |c Print |9 978-1-4684-0135-6 | ||
| 024 | 7 | |a 10.1007/978-1-4684-0133-2 |2 doi | |
| 035 | |a (OCoLC)863882084 | ||
| 035 | |a (DE-599)BVBBV042421007 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.7 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Washington, Lawrence C. |d 1951- |e Verfasser |0 (DE-588)1033730076 |4 aut | |
| 245 | 1 | 0 | |a Introduction to Cyclotomic Fields |c by Lawrence C. Washington |
| 264 | 1 | |a New York, NY |b Springer US |c 1982 | |
| 300 | |a 1 Online-Ressource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 83 |x 0072-5285 | |
| 500 | |a This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Algebraischer Zahlkörper |0 (DE-588)4068537-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kreiskörper |0 (DE-588)4165607-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kreiskörper |0 (DE-588)4165607-6 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Algebraischer Zahlkörper |0 (DE-588)4068537-8 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4684-0133-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856424 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153093568331776 |
|---|---|
| any_adam_object | |
| author | Washington, Lawrence C. 1951- |
| author_GND | (DE-588)1033730076 |
| author_facet | Washington, Lawrence C. 1951- |
| author_role | aut |
| author_sort | Washington, Lawrence C. 1951- |
| author_variant | l c w lc lcw |
| building | Verbundindex |
| bvnumber | BV042421007 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863882084 (DE-599)BVBBV042421007 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-0133-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03474nmm a2200553zcb4500</leader><controlfield tag="001">BV042421007</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160714 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1982 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468401332</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4684-0133-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468401356</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4684-0135-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4684-0133-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863882084</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421007</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Washington, Lawrence C.</subfield><subfield code="d">1951-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1033730076</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to Cyclotomic Fields</subfield><subfield code="c">by Lawrence C. Washington</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer US</subfield><subfield code="c">1982</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">83</subfield><subfield code="x">0072-5285</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraischer Zahlkörper</subfield><subfield code="0">(DE-588)4068537-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kreiskörper</subfield><subfield code="0">(DE-588)4165607-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Zahlentheorie</subfield><subfield code="0">(DE-588)4001170-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kreiskörper</subfield><subfield code="0">(DE-588)4165607-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Algebraische Zahlentheorie</subfield><subfield code="0">(DE-588)4001170-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Algebraischer Zahlkörper</subfield><subfield code="0">(DE-588)4068537-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4684-0133-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856424</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042421007 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468401332 9781468401356 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856424 |
| oclc_num | 863882084 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer US |
| record_format | marc |
| series2 | Graduate Texts in Mathematics |
| spelling | Washington, Lawrence C. 1951- Verfasser (DE-588)1033730076 aut Introduction to Cyclotomic Fields by Lawrence C. Washington New York, NY Springer US 1982 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 83 0072-5285 This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2 Mathematics Number theory Number Theory Mathematik Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Kreiskörper (DE-588)4165607-6 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Kreiskörper (DE-588)4165607-6 s 1\p DE-604 Algebraische Zahlentheorie (DE-588)4001170-7 s 2\p DE-604 Algebraischer Zahlkörper (DE-588)4068537-8 s 3\p DE-604 https://doi.org/10.1007/978-1-4684-0133-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Washington, Lawrence C. 1951- Introduction to Cyclotomic Fields Mathematics Number theory Number Theory Mathematik Algebraischer Zahlkörper (DE-588)4068537-8 gnd Kreiskörper (DE-588)4165607-6 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4068537-8 (DE-588)4165607-6 (DE-588)4001170-7 |
| title | Introduction to Cyclotomic Fields |
| title_auth | Introduction to Cyclotomic Fields |
| title_exact_search | Introduction to Cyclotomic Fields |
| title_full | Introduction to Cyclotomic Fields by Lawrence C. Washington |
| title_fullStr | Introduction to Cyclotomic Fields by Lawrence C. Washington |
| title_full_unstemmed | Introduction to Cyclotomic Fields by Lawrence C. Washington |
| title_short | Introduction to Cyclotomic Fields |
| title_sort | introduction to cyclotomic fields |
| topic | Mathematics Number theory Number Theory Mathematik Algebraischer Zahlkörper (DE-588)4068537-8 gnd Kreiskörper (DE-588)4165607-6 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Algebraischer Zahlkörper Kreiskörper Algebraische Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4684-0133-2 |
| work_keys_str_mv | AT washingtonlawrencec introductiontocyclotomicfields |