# Formal groups, supersingular abelian varieties and tame ramification - Mathematics > Number Theory

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

Author: Sara Arias-de-Reyna

Source: https://arxiv.org/