Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
COMPACTIFICATIONS OF LOG MORPHISMS
ELMAR GROSSE-KLÖNNE
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2004 年 56 巻 1 号 p. 79-104

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We introduce the notion of a relative log scheme with boundary: a morphism of log schemes together with a (log schematically) dense open immersion of its source into a third log scheme. The sheaf of relative log differentials naturally extends to this compactification and there is a notion of smoothness for such data. We indicate how this weak sort of compactification may be used to develop useful de Rham and crystalline cohomology theories for semistable log schemes over the log point over a field which are not necessarily proper.

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© 2004 by THE TOHOKU UNIVERSITY
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