STNB2019 (33rd edition)
Invariants of algebraic elements over henselian fields
Presenters
Nathália Moraes de Oliveira
Abstract
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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