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Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ ofa discrete valuation ring $R$. Assume that the residue field $k$ of $R$ isperfect and that $\mathop{\textrm{char}} k \neq 2$. Assume that the Weierstrasspoints of $C$ are $K$-rational. Let $S = \mathop{\textrm{Spec}} R$. Let$\mathcal{X}$ be the minimal proper regular model of $C$ over $S$. Let$\mathop{\textrm{Art}} (\mathcal{X}/S)$ denote the Artin conductor of the$S$-scheme $\mathcal{X}$ and let $\nu (\Delta)$ denote the minimal discriminantof $C$. We prove that $-\mathop{\textrm{Art}} (\mathcal{X}/S) \leq \nu(\Delta)$. As a corollary, we obtain that the number of components of thespecial fiber of $\mathcal{X}$ is bounded above by $\nu(\Delta)+1$.

Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points