David, Carchedi, Sarah, Scherotzke, Nicolò, Sibilla, Mattia, Talpo (2017) KatoNakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes. Geometry & Topology, 21 (5). pp. 30933158. ISSN 13640380. (doi:10.2140/gt.2017.21.3093)
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Official URL http://dx.doi.org/10.2140/gt.2017.21.3093 
Abstract
For a log scheme locally of finite type over C, a natural candidate for its profinite homotopy type is the profinite completion of its KatoNakayama space. Alternatively, one may consider the profinite homotopy type of the underlying topological stack of its infinite root stack. Finally, for a log scheme not necessarily over C, another natural candidate is the profinite \'etale homotopy type of its infinite root stack. We prove that, for a fine saturated log scheme locally of finite type over C, these three notions agree. In particular, we construct a comparison map from the KatoNakayama space to the underlying topological stack of the infinite root stack, and prove that it induces an equivalence on profinite completions. In light of these results, we define the profinite homotopy type of a general fine saturated log scheme as the profinite \'etale homotopy type of its infinite root stack.
Item Type:  Article 

DOI/Identification number:  10.2140/gt.2017.21.3093 
Subjects:  Q Science > QA Mathematics (inc Computing science) 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science 
Depositing User:  Nicolo Sibilla 
Date Deposited:  31 May 2017 13:44 UTC 
Last Modified:  16 Jan 2020 15:59 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/61900 (The current URI for this page, for reference purposes) 
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