We determine which isogeny classes of supersingular abeliansurfaces over a finite field $k$ of characteristic $2$ containjacobians. We deal with this problem in a direct way by computingexplicitly the zeta function of all supersingular curves of genus$2$. Our procedure is constructive, so that we are able to exhibitcurves with prescribed zeta function and find formulas for thenumber of curves, up to $k$-isomorphism, leading to the same zetafunction.
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机译：我们确定特征性$ 2 $ containjacobians的有限域$ k $上哪些超异形abeliansurfaces的同系类。我们通过直接计算所有$ 2 $超奇异曲线的zeta函数来直接处理此问题。我们的过程是建设性的，因此我们能够展示具有规定zeta函数的曲线，并找到直至$ k $同构的曲线数量的公式，从而得出相同的zeta函数。
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