STNB2019 (33è any)

Invariants of algebraic elements over henselian fields


Nathália Moraes de Oliveira


Let $(K,v)$ be a henselian field and fix an algebraic element $\theta\in\overline{K}$ with $\deg(\alpha)=n$. Using the connexion between inductive valuations and Okutsu frames, we reobtain some results on the computation of invariants of tame algebraic elements over henselian fields. In this talk we will also explain when the set

$\lbrace v(\theta-\alpha)\mid \alpha\in\overline{K},\ \deg_K(\alpha) < n \rbrace$

contains a maximal value. The maximum of this set is called the main invariant of $\theta$.


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