Interpolation over ZZ and torsion in class groups
Commutative Algebra
2020-09-24 v2 Number Theory
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.
Cite
@article{arxiv.1905.12097,
title = {Interpolation over ZZ and torsion in class groups},
author = {John Berman and Daniel Erman},
journal= {arXiv preprint arXiv:1905.12097},
year = {2020}
}
Comments
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