1999/07/20 by Fumiharu Kato, Kato, Fumiharu · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/9907124
openalex publication_date 1999/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss log blow-up's, introduced by Kazuya Kato, and define the concept of log modifications. Using this concept we prove that any morphism f: X ---> Y of locally noetherian fs log schemes with underlying structures of f and Y quasi-compact can be modified to an exact morphism, and moreover to an integral morphism. By a well-known fact on the underlying structure of an integral morphism this result can be considered as a weak log-version of flattening theorem by Raynaud and Gruson.