Exactness, integrality, and log modifications

Details Exactness, integrality, and log modifications Exactness, integrality, and log modifications

1999-07-20

arxiv.org/abs/math/9907124v1

Mathematics

Algebraic Geometry

9 pages, LaTeX2e with amsfonts and amssymb

Scientific paper

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.

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