Mapping F_1-land:An overview of geometries over the field with one element

zbMath1271.14003arXiv0909.0069MaRDI QIDQ2904913

Oliver Lorscheid, Javier López Peña

Publication date: 24 August 2012

Full work available at URL: https://arxiv.org/abs/0909.0069

Mathematics Subject Classification ID

Arithmetic algebraic geometry (Diophantine geometry) (11G99) Generalizations (algebraic spaces, stacks) (14A20) Arithmetic problems in algebraic geometry; Diophantine geometry (14G99)

Related Items (26)

New foundations for geometry Two non-additive languages for arithmetical geometry ⋮ Deitmar schemes, graphs and zeta functions ⋮ The geometry of toric schemes ⋮ On the spectrum of monoids and semilattices. ⋮ Axiomatics as a Functional Strategy for Complex Proofs: The Case of Riemann Hypothesis ⋮ Endomotives of toric varieties ⋮ \(\mathbb{F}_{1}\) for everyone ⋮ The absolute Euler product representation of the absolute zeta function for a torsion free Noetherian \(\mathbb{F}_1\)-scheme ⋮ Quantum field theory over \(\mathbb F_1\) ⋮ Quadratic forms, compositions and triality over \(\mathbb F_1\) ⋮ A family of measures on symmetric groups and the field with one element ⋮ On quiver representations over \(\mathbb{F}_1\) ⋮ The topological shadow of \(\mathbb{F}_1\)-geometry: congruence spaces ⋮ IntroSurvey of representation theory ⋮ Projective geometry for blueprints ⋮ The hyperring of adèle classes ⋮ The structure of Deitmar schemes. I. ⋮ The hyperring of adèle classes ⋮ The geometry of blueprints. I: Algebraic background and scheme theory ⋮ Functor of points and height functions for noncommutative Arakelov geometry ⋮ Quasicoherent sheaves on projective schemes over \(\mathbb{F}_1\) ⋮ \(G \)-theory of \(\mathbb F_1\)-algebras I: the equivariant Nishida problem ⋮ Arithmetic of character varieties of free groups ⋮ A unified construction of semiring-homomorphic graph invariants ⋮ Sheaves and \(K\)-theory for \(\mathbb F_1\)-schemes ⋮ Picard groups for tropical toric schemes

This page was built for publication: Mapping F_1-land:An overview of geometries over the field with one element