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St. Petersburg Mathematical Journal

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The $ \mathbb{Z}_p$-rank of a topological $ K$-group


Author: O. Yu. Ivanova
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 20 (2008), nomer 4.
Journal: St. Petersburg Math. J. 20 (2009), 569-591
MSC (2000): Primary 11S70
DOI: https://doi.org/10.1090/S1061-0022-09-01062-0
Published electronically: June 1, 2009
MathSciNet review: 2473745
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Abstract | References | Similar Articles | Additional Information

Abstract: A complete two-dimensional local field $ K$ of mixed characteristic with finite second residue field is considered. It is shown that the rank of the quotient $ U(1)K_2^{\mathrm{top}}K/T_K$, where $ T_K$ is the closure of the torsion subgroup, is equal to the degree of the constant subfield of $ K$ over $ \mathbb{Q}_p$. Also, a basis of this quotient is constructed in the case where there exists a standard field $ L$ containing $ K$ such that $ L/K$ is an unramified extension.


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Additional Information

O. Yu. Ivanova
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, 198504 St. Petersburg, Russia
Email: olgaiv80@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-09-01062-0
Keywords: Second topological $K$-group, local field, torsion
Received by editor(s): December 21, 2007
Published electronically: June 1, 2009
Article copyright: © Copyright 2009 American Mathematical Society