Abstract. Let C be a hyperelliptic curve of genus g ≥ 1 over a discrete valuation field K. In this article we study the models of C over the ring of integers 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 O K dominates every minimal Weierstrass model. Some classical facts concerning Weierstrass models over O K of elliptic curves are generalized to hyperelliptic curves, and some others are proved in this new setting.
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