English

Zeta functions of supersingular curves of genus 2

Number Theory 2007-05-23 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0408383,
  title  = {Zeta functions of supersingular curves of genus 2},
  author = {Daniel Maisner and Enric Nart},
  journal= {arXiv preprint arXiv:math/0408383},
  year   = {2007}
}

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23 pages