×

On \(p\)-extensions of multidimensional local fields. (English) Zbl 0794.11043

The maximal \(p\)-extension of a local field of dimension \(n>1\) is much more complicated than in the case \(n=1\). The authors demonstrate this in computing the relations for the Galois group of the maximal \(p\)-extension of \(\mathbb{Q}_ p (\xi_ p) \{\{t\}\}\) modulo third commutators.
Reviewer: H.Koch (Berlin)

MSC:

11S15 Ramification and extension theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Demushkin, Maxima] p-extension of a local field, Izvestia Acad. Nauk 25 pp 329– (1961)
[2] Iwasawa, On Galois groups of local fields, Trans. Amer. Math. Soc. 80 pp 448– (1955) · Zbl 0074.03101
[3] Jannsen, Über Galoisgruppen lokaler Körper, Invent. Math. 70 pp 53– (1982) · Zbl 0534.12009
[4] Jannsen, Die Structur der absoluten Galoisgruppe p-adischer Zahlkörper, Invent. Math. 70 pp 70– (1982) · Zbl 0534.12010
[5] Kato, A generalization of local class field theory by using K-groups 1, J. Fac. Sci. Univ. Tokio, Sect. 1A 26 pp 303– (1979) · Zbl 0428.12013
[6] Koch, Über Darstellungsräume und die Structur der multiplicativen Gruppe eines p-adischen Zahlkörpers, Math. Nachr. 26 pp 67– (1963) · Zbl 0124.27102
[7] Koch, Galoissche Theorie der p-Erweiterungen (1970)
[8] Koch, Über Galoissche Gruppen von p-adischen Zahlkörpern, Math. Nachr. 29 pp 77– (1965) · Zbl 0128.26401
[9] Merkurjev, K-cohomology of Severi-Brauer varieties and norm residue homomorphism, Izvestia Acad. Nauk 46 pp 1011– (1982)
[10] Parshin, Class field theory and algebraic K-theory, Uspekhi Mat. Nauk 30 pp 253– (1975)
[11] Parshin, Local class field theory, Trudy Mat. Inst. Steklov 165 pp 143– (1984) · Zbl 0535.12013
[12] Safarevic, On p-extensions, Mat. Sbornik 20 pp 351– (1947)
[13] Vostokov, The explicit construction of class field theory for multidimensional local fields, Izvestia Acad. Nauk 49 pp 283– (1985)
[14] Vostokov, On the theory of multidimensional local fields. Methods and constructions, Algebra i Analis 2 pp 91– (1990)
[15] Wingberg, Der Eindeutigkeitssatz für Demushkinformationen, Invent. Math. 70 pp 99– (1982)
[16] Yakovlev, The Galois group of an algebraic closure of local fields, Izvestia Acad. Nauk 32 pp 1283– (1968)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.