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.
Logarithmically Regular Morphisms / Molcho, S; Temkin, M. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - (2021). [10.1007/s00208-020-02116-z]
Logarithmically Regular Morphisms
Molcho S;
2021
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’s chart criterion of logarithmic smoothness.File allegati a questo prodotto
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