V. Alexandru, M. Vâjâitu, A. Zaharescu: Isometric Galois actions over $p$-adic fields, p. 295-301

Abstract:

Let $p$ be a prime number, $\Bbb Q_p$ the field of $p$-adic numbers, $\overline {\Bbb Q}_p$ a fixed algebraic closure of $\Bbb Q_p$ and $\Bbb C_p$ the completion of $\overline {\Bbb Q}_p$ with respect to the $p$-adic valuation. Let $G_p=Gal_{cont}(\Bbb C_p/\Bbb Q_p)$ be the group of continuous automorphisms of $\Bbb C_p$ over $\Bbb Q_p$. We investigate isometric Galois actions of the Galois group $G_p$ on subsets of $\Bbb C_p$.

Key Words and phrases: Galois actions, $p$-adic fields, isometries

2010 Mathematics Subject Classification: 11S99

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