Deitmar's versus Toën-Vaquié's schemes over \({\mathbb{F}_{1}}\)

DOI10.1007/s00209-011-0896-5zbMath1268.14005arXiv1005.0287OpenAlexW3122240866MaRDI QIDQ444196

Alberto Vezzani

Publication date: 13 August 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.0287

zbMATH Keywords

field with one element\({\mathbb {F}_{1}}\)-geometrycommutative algebra of monoidsspectrum of monoids

Mathematics Subject Classification ID

Generalizations (algebraic spaces, stacks) (14A20) Schemes and morphisms (14A15)

Related Items (11)

Čech cohomology over \(\mathbb{F}_{1^2}\) ⋮ The geometry of toric schemes ⋮ Endomotives of toric varieties ⋮ Čech cohomology of semiring schemes ⋮ Picard groups and class groups of monoid schemes ⋮ Can We Dream of a 1-Adic Langlands Correspondence? ⋮ The topological shadow of \(\mathbb{F}_1\)-geometry: congruence spaces ⋮ Smoothness in Relative Geometry ⋮ Blue schemes, semiring schemes, and relative schemes after Toën and Vaquié ⋮ A topological groupoid representing the topos of presheaves on a monoid ⋮ Some remarks on blueprints and \(\mathbb{F}_1\)-schemes

Cites Work

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• Sheaves in geometry and logic: a first introduction to topos theory
• New Approach to Arakelov Geometry
• Toric Singularities
• Projective Geometry over  1 and the Gaussian Binomial Coefficients
• Au-dessous de Specℤ
• Categories and Sheaves
• Autour de la platitude

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