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Inverting log blowups in log geometry

Doosung Park

Vol. 6 (2024), No. 3, 405–453
Abstract

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
Mathematical Subject Classification
Primary: 14A21
Milestones
Received: 23 March 2023
Revised: 20 April 2024
Accepted: 7 May 2024
Published: 30 September 2024
Authors
Doosung Park
Department of Mathematics and Informatics
Bergische Universität Wuppertal
Wuppertal
Germany