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

Kurihara classification and maximal depth extensions for multidimensional local fields


Author: O. Yu. Ivanova
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 24 (2012), nomer 6.
Journal: St. Petersburg Math. J. 24 (2013), 877-901
MSC (2010): Primary 11F85
Published electronically: September 23, 2013
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Abstract: Multidimensional local fields of mixed characteristic with finite last residue field are considered. For each field and a set of its local parameters, a quantity $ \Delta $ is defined as the difference of the minimum valuation of the coefficients at the differentials of local parameters of the residue field and the valuation of the coefficient at the differential of the uniformizer in a linear relation between the local parameters. In terms of the theory of elimination of ramification, the fields are described for which $ \Delta $ attains its minimum for a fixed ramification index over the subfield of constants. The extreme values of $ \Delta $ for a fixed field are studied.


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Additional Information

O. Yu. Ivanova
Affiliation: St. Petersburg State University of aerospace instrumentation, Bolshaya Morskaya street 67, St. Petersburg 190000, Russia
Email: olgaiv80@mail.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01271-4
PII: S 1061-0022(2013)01271-4
Keywords: Local fields, elimination of ramification, module of differentials
Received by editor(s): May 12, 2012
Published electronically: September 23, 2013
Additional Notes: Supported by RFBR (grant no. 11-01-00588-a)
Article copyright: © Copyright 2013 American Mathematical Society