Categorical representation of locally Noetherian log schemes
type: Item
instance of: scholarly article
title: Categorical representation of locally Noetherian log schemes
zbMATH Open document ID: 1073.14002
author: Shinichi Mochizuki
published in: Advances in Mathematics
publication date: 2004-10-01T00:00:00Z
review text: The aim of this paper is to show that certain types of schemes can be recovered from categories associated to them. The author starts by studying the case of locally Noetherian schemes. To such a scheme \(X\), he associates the category \(\text{Sch}(X)\) of morphisms of finite type from Noetherian schemes to \(X\). He then shows step by step how to reconstruct \(X\) by purely categorical techniques from the category \(\text{Sch}(X)\). In the second part of the paper, this is extended to fine saturated log schemes whose underlying scheme is locally Noetherian. Here the appropriate category is the category of morphisms from fine saturated log schemes whose underlying scheme is Noetherian and which have the property that the underlying morphism of schemes is of finite type.
Mathematics Subject Classification ID: 14A15
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 18F99
zbMATH DE Number: 2105311
zbMATH Keywords: anabelian geometry
reviewed by: Andreas Cap
MaRDI profile type: Publication
full work available at URL: j.aim.2003.10.005
OpenAlex ID: W1975372149
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DOI: 10.1016/J.AIM.2003.10.005
description: scientific article; zbMATH DE number 2105311