Field Arithmetic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? |
| Beschreibung: | 1 Online-Ressource (XVII, 460 p) |
| ISBN: | 9783662072165 9783662072189 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-662-07216-5 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804153099088035840 |
|---|---|
| any_adam_object | |
| author | Fried, Michael D. |
| author_facet | Fried, Michael D. |
| author_role | aut |
| author_sort | Fried, Michael D. |
| author_variant | m d f md mdf |
| building | Verbundindex |
| bvnumber | BV042423390 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864002567 (DE-599)BVBBV042423390 |
| 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 | 3512.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-07216-5 |
| format | Electronic eBook |
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| id | DE-604.BV042423390 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662072165 9783662072189 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858807 |
| oclc_num | 864002567 |
| 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 (XVII, 460 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics |
| spelling | Fried, Michael D. Verfasser aut Field Arithmetic by Michael D. Fried, Moshe Jarden Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (XVII, 460 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics 11 0071-1136 Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? Mathematics Geometry, algebraic Field theory (Physics) Logic, Symbolic and mathematical Field Theory and Polynomials Mathematical Logic and Foundations Algebraic Geometry Mathematik Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraischer Körper (DE-588)4141852-9 gnd rswk-swf Proendliche Gruppe (DE-588)4132444-4 gnd rswk-swf Funktionenkörper (DE-588)4155688-4 gnd rswk-swf Pseudoalgebraisch abgeschlossener Körper (DE-588)4132443-2 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 gnd rswk-swf Absoluter Klassenkörper (DE-588)4132442-0 gnd rswk-swf Pseudoalgebraisch abgeschlossener Körper (DE-588)4132443-2 s Absoluter Klassenkörper (DE-588)4132442-0 s Proendliche Gruppe (DE-588)4132444-4 s 1\p DE-604 Algebraischer Zahlkörper (DE-588)4068537-8 s 2\p DE-604 Algebraische Zahlentheorie (DE-588)4001170-7 s 3\p DE-604 Algebraischer Funktionenkörper (DE-588)4141850-5 s 4\p DE-604 Funktionenkörper (DE-588)4155688-4 s 5\p DE-604 Algebraischer Körper (DE-588)4141852-9 s 6\p DE-604 Jarden, Moshe Sonstige oth https://doi.org/10.1007/978-3-662-07216-5 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fried, Michael D. Field Arithmetic Mathematics Geometry, algebraic Field theory (Physics) Logic, Symbolic and mathematical Field Theory and Polynomials Mathematical Logic and Foundations Algebraic Geometry Mathematik Algebraische Zahlentheorie (DE-588)4001170-7 gnd Algebraischer Körper (DE-588)4141852-9 gnd Proendliche Gruppe (DE-588)4132444-4 gnd Funktionenkörper (DE-588)4155688-4 gnd Pseudoalgebraisch abgeschlossener Körper (DE-588)4132443-2 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd Absoluter Klassenkörper (DE-588)4132442-0 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4141852-9 (DE-588)4132444-4 (DE-588)4155688-4 (DE-588)4132443-2 (DE-588)4068537-8 (DE-588)4141850-5 (DE-588)4132442-0 |
| title | Field Arithmetic |
| title_auth | Field Arithmetic |
| title_exact_search | Field Arithmetic |
| title_full | Field Arithmetic by Michael D. Fried, Moshe Jarden |
| title_fullStr | Field Arithmetic by Michael D. Fried, Moshe Jarden |
| title_full_unstemmed | Field Arithmetic by Michael D. Fried, Moshe Jarden |
| title_short | Field Arithmetic |
| title_sort | field arithmetic |
| topic | Mathematics Geometry, algebraic Field theory (Physics) Logic, Symbolic and mathematical Field Theory and Polynomials Mathematical Logic and Foundations Algebraic Geometry Mathematik Algebraische Zahlentheorie (DE-588)4001170-7 gnd Algebraischer Körper (DE-588)4141852-9 gnd Proendliche Gruppe (DE-588)4132444-4 gnd Funktionenkörper (DE-588)4155688-4 gnd Pseudoalgebraisch abgeschlossener Körper (DE-588)4132443-2 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd Absoluter Klassenkörper (DE-588)4132442-0 gnd |
| topic_facet | Mathematics Geometry, algebraic Field theory (Physics) Logic, Symbolic and mathematical Field Theory and Polynomials Mathematical Logic and Foundations Algebraic Geometry Mathematik Algebraische Zahlentheorie Algebraischer Körper Proendliche Gruppe Funktionenkörper Pseudoalgebraisch abgeschlossener Körper Algebraischer Zahlkörper Algebraischer Funktionenkörper Absoluter Klassenkörper |
| url | https://doi.org/10.1007/978-3-662-07216-5 |
| work_keys_str_mv | AT friedmichaeld fieldarithmetic AT jardenmoshe fieldarithmetic |