On unramified abelian extensions of a complete field under a discrete valuation with arbitrary residue field of characteristic p≠0 and its application to wildly ramified Zp-extensions

Hiroo MIKI

doi:10.2969/jmsj/02920363

On unramified abelian extensions of a complete field under a discrete valuation with arbitrary residue field of characteristic p≠0 and its application to wildly ramified Z_p-extensions

Hiroo MIKI

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JOURNAL FREE ACCESS

1977 Volume 29 Issue 2 Pages 363-371

DOI https://doi.org/10.2969/jmsj/02920363

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Published: 1977 Received: December 05, 1974 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. Artin and J. Tate, Class field theory, Benjamin, New York, 1967.
2) Y. Ihara, On a problem on some complete p-adic function fields (in Japanese), Kokyuroku of the Research Institute for Mathematical Sciences Kyoto Univ., 41 (1968), 7-17.
3) S. Iyanaga (editors), Number theory (in Japanese), Iwanami Shoten, Tokyo, 1969=(in English), North-Holland, Amsterdam, 1975.
4) S. MacLane, Subfields and automorphism groups of p-adic fields, Ann. of Math., 40 (1939), 424-442.
5) H. Miki, On cyclic extensions of p-power degree over complete p-adic fields (in Japanese), Master's thesis, University of Tokyo, 1973.
6) H. Miki, On Z_p-extensions of complete p-adic power series fields and function fields, J. Fac. Sci. Univ. Tokyo Sec. IA, 21 (1974), 377-393.
7) S. Sen, On automorphisms of local fields, Ann. of Math., 90 (1969), 33-46.
8) J. P. Serre, Corps locaux (2nd edition), Hermann, Paris, 1968.
9) O. Teichmüller, Diskret bewertete perfekte Körper mit unvollkommenem Rest- klassenkörper, J. Reine Angew. Math., 176 (1937), 141-152.
10) E. Witt, Zyklische Körper und Algebren der Characteristik p von Grade pⁿ, J. Reine Angew. Math., 176 (1936), 126-140.

Right : [1] E. Artin and J. Tate, Class field theory, Benjamin, New York, 1967.
[2] Y. Ihara, On a problem on some complete p-adic function fields (in Japanese), Kokyuroku of the Research Institute for Mathematical Sciences Kyoto Univ., 41 (1968), 7-17.
[4] S. MacLane, Subfields and automorphism groups of p-adic fields, Ann. of Math., 40 (1939), 424-442.
[5] H. Miki, On cyclic extensions of p-power degree over complete p-adic fields (in Japanese), Master's thesis, University of Tokyo, 1973.
[6] H. Miki, On Z_p-extensions of complete p-adic power series fields and function fields, J. Fac. Sci. Univ. Tokyo Sec. IA, 21 (1974), 377-393.
[7] S. Sen, On automorphisms of local fields, Ann. of Math., 90 (1969), 33-46.
[8] J. P. Serre, Corps locaux (2nd edition), Hermann, Paris, 1968.
[9] O. Teichmüller, Diskret bewertete perfekte Körper mit unvollkommenem Restklassenkörper, J. Reine Angew. Math., 176 (1937), 141-152.
[10] E. Witt, Zyklische Körper und Algebren der Characteristik p von Grade pⁿ, J. Reine Angew. Math., 176 (1936), 126-140.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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