Ramification of p-power torsion points of formal groups

Let p be a rational prime, let F denote a finite, unramified extension of Qp , let K be the completion of the maximal unramified extension of Qp , and let K¯ be some fixed algebraic closure of K. Let A be an abelian variety defined over F, with good reduction, let A denote the Néron model of A over Spec (OF) , and let A^ be the formal completion of A along the identity of its special fiber, i.e. the formal group of A. In this work, we prove two results concerning the ramification of p-power torsion points on A^ . One of our main results describes conditions on A^ , base changed to Spf (OK) , for which the field K(A^ [p]) / K i s a tamely ramified extension where A^ [p] denotes the group of p-torsion points of A^ over OK¯ . This result generalizes previous work when A is 1-dimensional and work of Arias-de-Reyna when A is the Jacobian of certain genus 2 hyperelliptic curves.