Zeta functions of supersingular curves of genus 2

Details Zeta functions of supersingular curves of genus 2 Zeta functions of supersingular curves of genus 2

2004-08-27

arxiv.org/abs/math/0408383v1

Mathematics

Number Theory

23 pages

Scientific paper

We determine what 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 to count the number of curves, up to k-isomorphism, leading to the same zeta function.

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