Resolution of embedded toric $\mathrm{\Lambda }$-schemes

A key example in Borger’s theory of $\mathrm{\Lambda }$-structure is toric $\mathrm{\Lambda }$-structure. We prove a resolution of singularities result for embedded toric $\mathrm{\Lambda }$-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.