Relative desingularization and principalization of ideals
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.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Publication details
- Journal / source
- Publications mathématiques de l IHÉS
- Publisher
- MathDoc/Centre Mersenne
- Pages
- 1–103
- Publication date
- 2 September 2026
- Language
- EN