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Bibliographic Details
Main Author: Machida, Kai
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.04271
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author Machida, Kai
author_facet Machida, Kai
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_04271
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Order reduction of $Λ$-marked monomial ideals and weak resolutions
Machida, Kai
Algebraic Geometry
14E15
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.
title Order reduction of $Λ$-marked monomial ideals and weak resolutions
topic Algebraic Geometry
14E15
url https://arxiv.org/abs/2505.04271