The ℤ_{𝕡}-rank of a topological 𝕂-group

Ivanova, O.

doi:10.1090/S1061-0022-09-01062-0

The $\mathbb Z_p$-rank of a topological $K$-group
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by O. Yu. Ivanova
Translated by: B. M. Bekker

St. Petersburg Math. J. 20 (2009), 569-591

DOI: https://doi.org/10.1090/S1061-0022-09-01062-0

Published electronically: June 1, 2009

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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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