Groups of automorphisms of local fields of period pM and nilpotent class < p

Abstract

Suppose K is a finite field extension of ℚpcontaining a pm-th primitive root of unity. For 1 ≤ s eK(M + s/(p - 1)) - (1 - δis)/p, where eKis the ramification index of K and δ1sis the Kronecker symbol.