A henselian preparation theorem

TL;DR

This paper establishes a henselian version of the Weierstrass preparation theorem, extending local results to henselian pairs, and introduces a henselian analogue of the p-adic resultant, broadening algebraic tools in henselian contexts.

Contribution

It generalizes the Weierstrass preparation theorem to henselian pairs and constructs a henselian analogue of the p-adic resultant, expanding algebraic methods in henselian settings.

Findings

Proved a henselian analogue of the Weierstrass preparation theorem.

Constructed a henselian analogue of the p-adic resultant.

Extended algebraic tools for henselian pairs.

Abstract

We prove an analogue of the Weierstrass preparation theorem for henselian pairs, generalizing the local case recently proved by Bouthier and {\v C}esnavi{\v c}ius. As an application, we construct a henselian analogue of the resultant of p-adic series defined by Berger.