Construction of continuous idele class characters in quadratic number fields, and imbedding problems for dihedral and quaternion fields

Franz Halter-Koch

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1975-1976)

  • Volume: 17, Issue: 1, page 1-13

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Halter-Koch, Franz. "Construction of continuous idele class characters in quadratic number fields, and imbedding problems for dihedral and quaternion fields." Séminaire Delange-Pisot-Poitou. Théorie des nombres 17.1 (1975-1976): 1-13. <http://eudml.org/doc/110912>.

@article{Halter1975-1976,
author = {Halter-Koch, Franz},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
keywords = {Imbedding Problem; Galois Extension; Grunwald-Wang Theorem; Idele Class Character; Class Field Theory; Local-Global Principle},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Secrétariat mathématique},
title = {Construction of continuous idele class characters in quadratic number fields, and imbedding problems for dihedral and quaternion fields},
url = {http://eudml.org/doc/110912},
volume = {17},
year = {1975-1976},
}

TY - JOUR
AU - Halter-Koch, Franz
TI - Construction of continuous idele class characters in quadratic number fields, and imbedding problems for dihedral and quaternion fields
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1975-1976
PB - Secrétariat mathématique
VL - 17
IS - 1
SP - 1
EP - 13
LA - eng
KW - Imbedding Problem; Galois Extension; Grunwald-Wang Theorem; Idele Class Character; Class Field Theory; Local-Global Principle
UR - http://eudml.org/doc/110912
ER -

References

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  1. [1] Damey ( P.) et Martinet ( J.). - Plongement d'une extension quadratique dans une extension quaternionienne, J. für reine und angew. Math., t. 262/263, 1973, p. 323-338. Zbl0297.12010MR330104
  2. [2] Fröhlich ( A.). - A rational characterisation of certain sets of relatively abelian extensions, Phil. Trans. royal Soc. London, Series A, t. 251, 1959, p. 385-425. Zbl0098.03402MR108480
  3. [3] Halter-Koch ( F.). - Arithmetische Theorie der Normalkörper von 2-Potenzgrad mit Diedergruppe, J. of Number Theory, t. 3, 1971, p. 412-443. Zbl0229.12006MR285511
  4. [4] Halter-Koch ( F.). - Einseinheitengruppen und prime Restklassengruppen in quadratischen Zahlkörpern, J. of Number Theory, t. 4, 1972, p. 70-77. Zbl0229.12004MR296045
  5. [5] Hasse ( H.). - Zahlentheorie. 3te Aufl. - Berlin, Akademie Verlag, 1970. 
  6. [6] Hasse ( H.). - Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage, Math. Z., t. 31, 1930, p. 565-582. Zbl56.0167.02MR1545136JFM56.0167.02
  7. [7] Neukirch ( J.). - Über das Einbettungsproblem der algebraischen Zahlentheorie, Invent. Math., t. 21, 1973, p. 59-116. Zbl0267.12005MR337894
  8. [8] Poitou ( G.). - Einbettungsprobleme mit abelschem Kern, Oberwolfach, 1975. 
  9. [9] Porusch ( I.). - Arithmetik in Zahlkörpern, deren zugehörige Galoissche Körper spezielle metabelsche Gruppen besitzen, auf klassenkörpertheoretischer Grundlage, Math. Z., t. 37, 1933, p. 134-160. Zbl0006.25203MR1545387JFM59.0945.02
  10. [10] Richter ( H.). - Über die Lösbarkeit einiger nicht-abelscher Einbettungsprobleme, Math. Annalen, t. 112, 1936, p. 700-726. Zbl0014.24803MR1513070
  11. [11] Rosenbluth ( E.). - Die arithmetische Theorie und Konstruktion der Quaternionenkörper auf klassenkörpertheoretischer Grundlage, Monatsh. Math. Phys., t. 41, 1934, p. 85-125. Zbl0009.39202
  12. [12] Tate ( J.). - Global class field theory, "Algebraic number theory", p. 162-203. - New York, Academic Press, 1967. Zbl1179.11041MR220697

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