Some remarks on blueprints and \(\mathbb{F}_1\)-schemes
type: Item
instance of: scholarly article
title: Some remarks on blueprints and \(\mathbb{F}_1\)-schemes
zbMATH Open document ID: 1487.14007
author: Claudio Bartocci
author: Andrea Gentili
author: Jean-Jacques Szczeciniarz
published in: São Paulo Journal of Mathematical Sciences
publication date: 2021-12-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1905.01183
review text: The authors review in this paper with great care 3 different approaches to \(\mathbb F_1\)-geometry, which are Toen-Vaquie's relative schemes, Lorscheid's blue schemes and Connes-Consani's \(\mathbb F_1\)-schemes. They explain certain adjunctions between monoids, rings and blueprints in detail and extend them to the corresponding categories of sheaves. These adjunctions allows them to merge blue schemes with Connes and Consani's notion of \(\mathbb F_1\)-schemes, which results in the category of so-called \(\mathbb F_1\)-schemes with relations as a common generalization.
reviewed by: Oliver Lorscheid
Mathematics Subject Classification ID: 14A23
Mathematics Subject Classification ID: 18M05
zbMATH DE Number: 7438678
zbMATH Keywords: \(\mathbb{F}_1\)-schemes
zbMATH Keywords: blueprints
zbMATH Keywords: relative algebraic geometry
Wikidata QID: Q122157226
MaRDI profile type: Publication
OpenAlex ID: W3179473941
arXiv ID: 1905.01183
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DOI: 10.1007/S40863-021-00221-8
description: scientific article