Fibers of flat morphisms and Weierstrass preparation theorem

TL;DR

This paper characterizes flat ring extensions satisfying the Weierstrass preparation theorem and extends the theorem to rings of functions on a normal curve over a local domain, generalizing recent results.

Contribution

It provides a new characterization of flat extensions satisfying the Weierstrass preparation theorem and proves a generalized version for rings of functions on a normal curve.

Findings

Characterization of flat extensions satisfying the Weierstrass preparation theorem

A generalized Weierstrass preparation theorem for rings on a normal curve

Alternative proof method compared to recent works

Abstract

We characterize flat extensions of commutative rings satisfying the Weierstrass preparation theorem. Using this characterization we prove a variant of the Weierstrass preparation theorem for rings of functions on a normal curve over a complete local domain of dimension one. This generalizes recent works of Harbater, Hartmann and Krashen with a different method of proof.