Logarithmically regular morphisms

Sam Molcho; Michael Temkin

doi:https://doi.org/10.1007/s00208-020-02116-z

Logarithmically regular morphisms

Sam Molcho, Michael Temkin

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the stack Log_X parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via Log_X, as defined by Olsson. We give a concrete combinatorial presentation of Log_X, and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato’s chart criterion of logarithmic smoothness.

Original language	English
Pages (from-to)	325-346
Number of pages	22
Journal	Mathematische Annalen
Volume	379
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-020-02116-z
State	Published - Feb 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Logarithmically regular morphisms",

abstract = "We consider the stack LogX parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via LogX, as defined by Olsson. We give a concrete combinatorial presentation of LogX, and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato{\textquoteright}s chart criterion of logarithmic smoothness.",

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AB - We consider the stack LogX parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via LogX, as defined by Olsson. We give a concrete combinatorial presentation of LogX, and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato’s chart criterion of logarithmic smoothness.

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SP - 325

EP - 346

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1-2

ER -

Logarithmically regular morphisms

Abstract

All Science Journal Classification (ASJC) codes

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