Formal groups, supersingular abelian varieties and tame ramification

Details Formal groups, supersingular abelian varieties and tame ramification Formal groups, supersingular abelian varieties and tame ramification

2009-10-07

arxiv.org/abs/0910.1212v1

Mathematics

Number Theory

22 pages

Scientific paper

Let us consider an abelian variety defined over $\mathbb{Q_{\ell}}$ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the $\ell$-torsion points of the variety is trivial. Furthermore we give a family of curves of genus 2 such that their Jacobian surfaces have good supersingular reduction and satisfy these conditions. We address this question by means of a detailed study of the formal group law attached to abelian varieties.

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