## 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 $\theta$.