Quelques remarques sur le champ des courbes hyperelliptiques en caracteristique deux

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Dans cette note on decrit le champ des courbes hyperelliptiques lisses defines sur un corps algebriquement clos de caracteristique deux comme un champ quotient. On en deduit le groupe de Picard. ----- In this note we describe the stack Hg of smooth hyperelliptic curves of genus g over an algebraically closed field of characteristic two, as a quotient stack of a smooth variety of dimension 3g+5 by a non reductive algebraic group, extending a well known result of Vistoli. As an application, we show the Mumford-Vistoli description of the Picard group of the stack Hg is valid in this characteristic. We also describe the natural stratification of Hg by means of higher ramification data. We point out that after stable compactification Hg is not smooth in codimension at least two.