Modèles entiers des courbes hyperelliptiques sur un corps de valuation discrète

Let $C$ be a hyperelliptic curve of genus $g\ge 1$ over a discrete valuation field $K$. In this article we study the models of $C$ over the ring of integers $\mathcal {O}_{K}$ of $K$. To each Weierstrass model (that is a projective model arising from a hyperelliptic equation of $C$ with integral coefficients), one can associate a (valuation of) discriminant. Then we give a criterion for a Weierstrass model to have minimal discriminant. We show also that in the most cases, the minimal regular model of $C$ over $\mathcal {O}_{K}$ dominates every minimal Weierstrass model. Some classical facts concerning Weierstrass models over $\mathcal {O}_{K}$ of elliptic curves are generalized to hyperelliptic curves, and some others are proved in this new setting.