Galois structure on integral valued polynomials

Abstract

We characterize finite Galois extensions $K$ of the field of rational numbers in terms of the rings ${\mathrm{Int}}_{\mathbb{Q}}({\mathcal{O}}_K)$, recently introduced by Loper and Werner, consisting of those polynomials which have coefficients in $\mathbb{Q}$ and such that $f({\mathcal{O}}_K)$ is contained in ${\mathcal{O}}_K$. We also address the problem of constructing a basis for ${\mathrm{Int}}_{\mathbb{Q}}({\mathcal{O}}_K)$ as a $\mathbb{Z}$-module.

final version, accepted for publication in J. Number Theory (2016). any comment is welcome