Vol. 1, No. 2, 2019

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Saturated morphisms of logarithmic schemes

Takeshi Tsuji

Vol. 1 (2019), No. 2, 185–220

The notion of universally saturated morphisms between saturated log schemes was introduced by Kazuya Kato. In this paper, we study universally saturated morphisms systematically by introducing the notion of saturated morphisms between integral log schemes as a relative analogue of saturated log structures. We eventually show that a morphism of saturated log schemes is universally saturated if and only if it is saturated. We prove some fundamental properties and characterizations of universally saturated morphisms via this interpretation.

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logarithmic structure, logarithmic scheme, saturated morphism
Mathematical Subject Classification 2010
Primary: 06F05, 14A15
Received: 10 October 2017
Revised: 1 February 2018
Accepted: 15 February 2018
Published: 14 May 2018
Takeshi Tsuji
Graduate School of Mathematical Sciences
The University of Tokyo
Tokyo 153-8914