Geodesic
Zeta Functions of Supersingular Curves of Genus 2
Canadian journal of mathematics, Tome 59 (2007) no. 2, pp. 372-392

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We determine which isogeny classes of supersingular abelian surfaces over a finite field $k$ of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to $k$ -isomorphism, leading to the same zeta function.
DOI : 10.4153/CJM-2007-016-6
Mots-clés : 11G20, 14G15, 11G10 
Maisner, Daniel; Nart, Enric. Zeta Functions of Supersingular Curves of Genus 2. Canadian journal of mathematics, Tome 59 (2007) no. 2, pp. 372-392. doi: 10.4153/CJM-2007-016-6
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