Kevin Keating

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19982003

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math.NT2003

Extensions of local fields and truncated power series

Kevin Keating

Let $K$ be a finite tamely ramified extension of $\Q_p$ and let $L / K$ be a totally ramified $(Z / p^{n} Z)$ -extension. Let $π_{L}$ be a uniformizer for $L$ , let $σ$ be a generator for $…

math.NT2001

Enumeration of Isomorphism Classes of Extensions of p-adic Fields

Xiang-dong Hou, Kevin Keating

Let $Ω$ be an algebraic closure of $Q_{p}$ and let $F$ be a finite extension of $Q_{p}$ contained in $Ω$ . Given positive integers $f$ and $e$ , the number of extensi…