Roots of Generalized Schönemann Polynomials in Henselian Extension Fields

  title={Roots of Generalized Sch{\"o}nemann Polynomials in Henselian Extension Fields},
  author={Ron Brown},
We study generalized Schönemann polynomials over a valued field F . If such a polynomial f is tame (i.e., a root of f generates a tamely ramified extension of F ), we give a best-possible criterion for when the existence in a Henselian extension field K of an approximate root of f guarantees the existence of an exact root of f in the extension field K. Let (F, v) be a valued field with residue class field F , value group vF , and valuation ring A. For any a ∈ A and polynomial h ∈ A[x] we let a… CONTINUE READING