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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On the relationship between Kurihara's classification and the theory of ramification removal


Author: O. Yu. Ivanova
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 24 (2012), nomer 2.
Journal: St. Petersburg Math. J. 24 (2013), 283-299
MSC (2010): Primary 11S15
Published electronically: January 22, 2013
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Abstract: A complete two-dimensional mixed-characteristic local field with finite second residue field is considered. It is proved that such a field is standard if and only if the difference between the valuations of the coefficients of a linear relation between local parameters is infinite for some choice of local parameters; the field in question is almost standard if and only if the above-mentioned difference can be made arbitrarily large by changing local parameters. In the case where a given field can be extended to a standard field by a fierce extension of prime degree, the field type in Kurihara's classification is proved to depend only on the ratio of the ramification jumps of these fields over their maximal standard subfields.


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Additional Information

O. Yu. Ivanova
Affiliation: St. Petersburg State University of Aerospace Instrumentation, Bolshaya morskaya st. 67, Saint Petersburg 190000, Russia
Email: olgaiv80@mail.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01239-8
PII: S 1061-0022(2013)01239-8
Keywords: Local fields, ramification removal, module of differentials
Received by editor(s): March 3, 2011
Published electronically: January 22, 2013
Additional Notes: The author was supported by RFBR (grant no. 11-01-00588)
Article copyright: © Copyright 2013 American Mathematical Society