TY - JOUR
T1 - Logarithmically regular morphisms
AU - Molcho, Sam
AU - Temkin, Michael
N1 - Publisher Copyright:
© 2020, The Author(s).
PY - 2021/2
Y1 - 2021/2
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85096394740&partnerID=8YFLogxK
U2 - 10.1007/s00208-020-02116-z
DO - 10.1007/s00208-020-02116-z
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AN - SCOPUS:85096394740
SN - 0025-5831
VL - 379
SP - 325
EP - 346
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -