On the norm maps of formal groups for Zp-extensions

Abstract

Let K be a finite extension of Q p and F (X, Y ) be a formal group defined over O K where O K is the ring of integers of K. For an arbitrary Z p -extensions K ∞ /K and the nth layer K n , we study the index [F (K n−1 ) : F -N K n /K n−1 (F (K n ))]. We give the asymptotic behavior of the index as n → ∞, and determine the index in several cases.