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Abstract
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In the category of log schemes, it is unclear how to define the blowups for nonstrict
closed immersions. We introduce the notion of divided log spaces. We obtain the
category of divided log spaces by locally inverting log blowups in the category of log
schemes. We show that blowups exist for closed immersions of log smooth divided log
spaces. This is an ingredient of the motivic six-functor formalism for log
schemes.
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Keywords
log schemes, log blowups, divided log spaces
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Mathematical Subject Classification
Primary: 14A21
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Milestones
Received: 23 March 2023
Revised: 20 April 2024
Accepted: 7 May 2024
Published: 30 September 2024
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