arXiv subjects
Publications and source records attributed to Kai Machida.
A key example in Borger's theory of $Λ$-structure is toric $Λ$-structure. We prove a resolution of singularities result for embedded toric $Λ$-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.
Borger's theory of $Λ$-spaces imbues algebraic spaces, which include schemes, with an additional structure defined by an extension of the Witt vector functor. Motivated by $\mathbb{F}_1$-geometry, we prove the existence of a weak resolution of singularities in the category of $Λ$-schemes. Our arguments are based on standard arguments in characteristic $0$ using the order reduction of an ideal marked with $Λ$-equivariant data. This paper is based on work from the author's PhD thesis.