Formal groups, supersingular abelian varieties and tame ramification

Let us consider an abelian variety defined over ${\mathbb{Q}}_{\mathbb{\ell }}$ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the $\mathrm{\ell }$-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.