Work

Relative desingularization and principalization of ideals

Year: 2026

Type: article

Abstract: In characteristic 0 , we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are relatively canonical and even functorial with respect to logarithmically regular morphisms and arbitrary base changes. Relative canonicity means that the principalization requires a fine enough non-canonical modification of the base, and once it is chosen the process is canonical. As a consequence we deduce the semistable reduction theorem over arbitrary valuation rings.

Source: Publications mathématiques de l IHÉS

DOI: 10.5802/pmihes.29

Authors: Dan Abramovich, Michael Temkin, Jarosław Włodarczyk

Institutions: Brown University, Hebrew University of Jerusalem, Purdue University West Lafayette

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,590

Funder: National Science Foundation