Interpolation over ZZ and torsion in class groups

Abstract

We prove an interpolation result for homogeneous polynomials over the integers, or more generally for PIDs with finite residue fields. Previous proofs of this result use the well-known but nontrivial fact that class groups of rings of integers are torsion. In this short note, we provide an independent proof using elementary techniques.

6 pages. In the previous version, the proof of Theorem 0.4 suffered from a significant error. We thank Aurel Page for pointing this out to us