  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.
