A characterization of Eisenstein polynomials generating extensions of degree and cyclic of degree over an unramified -adic field
Let be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree over , and extend it to when the base fields is an unramified extension of . When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We derive a complete...