Abstract
AbstractWe consider the stack $${\mathcal {L}}og_{X}$$
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o
g
X
parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via $${\mathcal {L}}og_{X}$$
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o
g
X
, as defined by Olsson. We give a concrete combinatorial presentation of $${\mathcal {L}}og_{X}$$
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g
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, 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.
Funder
European Research Council
Publisher
Springer Science and Business Media LLC
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