Resolution of embedded toric $\Lambda$-schemes

TL;DR

This paper proves a resolution of singularities for embedded toric $\Lambda$-schemes using an algorithm adapted from toric varieties over perfect fields, advancing the understanding of $\Lambda$-structures.

Contribution

It introduces a resolution of singularities specifically for embedded toric $\Lambda$-schemes, applying an existing algorithm in a new context.

Findings

Resolution of singularities for embedded toric $\Lambda$-schemes established

Algorithm of Bierstone and Milman successfully adapted to $\Lambda$-schemes

Enhances the understanding of toric $\Lambda$-structures in algebraic geometry

Abstract

A key example in Borger's theory of $\Lambda$-structure is toric $\Lambda$-structure. We prove a resolution of singularities result for embedded toric $\Lambda$-schemes by applying an algorithm of Bierstone and Milman for toric varieties over perfect fields. This paper is based on work from the author's PhD thesis.