On the notion of geometry over 𝔽₁

DOI10.1090/S1056-3911-2010-00535-8zbMath1227.14006arXiv0809.2926OpenAlexW1517991134MaRDI QIDQ3006591

Caterina Consani, Alain Connes

Publication date: 20 June 2011

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.2926

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Varieties over finite and local fields (11G25) Schemes and morphisms (14A15)

Related Items (27)

Arithmetic differential equations on \(\mathrm{GL}_n\). III: Galois groups ⋮ On absolute algebraic geometry the affine case ⋮ The Connes-Consani plane connection ⋮ The geometry of toric schemes ⋮ Toward a Galois theory of the integers over the sphere spectrum ⋮ On the Hall algebra of semigroup representations over \(\mathbb F_1\). ⋮ \(\mathbb{F}_{1}\) for everyone ⋮ Algebraic geometry over hyperrings ⋮ Towards the horizons of Tits's vision: on band schemes, crowds and \(\mathbb{F}_1\)-structures ⋮ Vector bundles on tropical schemes ⋮ A family of measures on symmetric groups and the field with one element ⋮ On the Hall algebra of coherent sheaves on \(\mathbb P^1\) over \(\mathbb F^1\) ⋮ Proto-exact categories of modules over semirings and hyperrings ⋮ On quiver representations over \(\mathbb{F}_1\) ⋮ Torified varieties and their geometries over \(\mathbb{F}_{1}\) ⋮ Hall Lie algebras of toric monoid schemes ⋮ Algebraic groups over the field with one element ⋮ The hyperring of adèle classes ⋮ The geometry of blueprints. I: Algebraic background and scheme theory ⋮ \(G \)-theory of \(\mathbb F_1\)-algebras I: the equivariant Nishida problem ⋮ Vector bundles over projective spaces. The case \({\mathbb F_1}\) ⋮ Numbers as functions ⋮ Cyclotomy and endomotives ⋮ THE GEOMETRY OF BLUEPRINTS PART II: TITS–WEYL MODELS OF ALGEBRAIC GROUPS ⋮ Derived schemes and the field with one element ⋮ On Noetherian schemes over (\mathcal{C},\otimes,1)$ and the category of quasi-coherent sheaves ⋮ Picard groups for tropical toric schemes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a representation of the idele class group related to primes and zeros of \(L\)-functions
• Noncommutative geometry, quantum fields and motives
• Fun with \(\mathbb F_1\)
• Buildings of spherical type and finite BN-pairs
• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
• Absolute derivations and zeta functions
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
• Quantum statistical mechanics over function fields
• Noncommutative geometry and motives: the thermodynamics of endomotives
• Normalisateurs de tores. I: Groupes de Coxeter etendus
• Number fields and function fields -- two parallel worlds
• Sur certains groupes simples
• New Approach to Arakelov Geometry
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Toric Singularities
• Non-additive geometry
• Au-dessous de Specℤ

This page was built for publication: On the notion of geometry over 𝔽₁