David Betzer

Affine Galois Realizations from Real Quadratic Units: Kummer Defects, Composita, and Radical Lattices

This preprint studies explicit Galois extensions arising from radicals of units in real quadratic fields. Let F/ℚ be a real quadratic field, let ε ∈ O_F× be a nonrational unit, and let ℓ ≥ 2. The associated trace–norm polynomial is Qε,ℓ(x) = (x^ℓ − ε)(x^ℓ − ε̄), where ε̄ denotes...