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  1. ; (, International Mathematics Research Notices)
    Abstract We prove an inequality between the conductor and the discriminant for all hyperelliptic curves defined over discretely valued fields $$K$$ with perfect residue field of characteristic not $$2$$. Specifically, if such a curve is given by $$y^{2} = f(x)$$ with $$f(x) \in \mathcal{O}_{K}[x]$$, and if $$\mathcal{X}$$ is its minimal regular model over $$\mathcal{O}_{K}$$, then the negative of the Artin conductor of $$\mathcal{X}$$ (and thus also the number of irreducible components of the special fiber of $$\mathcal{X}$$) is bounded above by the valuation of $$\operatorname{disc}(f)$$. There are no restrictions on genus of the curve or on the ramification of the splitting field of $$f$$. This generalizes earlier work of Ogg, Saito, Liu, and the second author. 
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  2. ; (, Research in Number Theory)
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  3. ; ; ; ; (, Journal de théorie des nombres de Bordeaux)
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