Homotopy types and geometries below Spec(ℤ)

DOI10.1090/conm/744/14978zbMath1504.14007arXiv1806.10801OpenAlexW3016333163MaRDI QIDQ3295989

Matilde Marcolli, Yuri I. Manin

Publication date: 3 July 2020

Published in: Dynamics: Topology and Numbers (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.10801

zbMATH Keywords

zeta functionsmotivic integrationGrothendieck ring of varietiesBost-Connes systemsWeil numbersgeometries below \(\mathrm{Spec}\mathbb{Z}\)quasi-unipotent endomorphisms

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Quantum equilibrium statistical mechanics (general) (82B10) Other Dirichlet series and zeta functions (11M41) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43) (Equivariant) Chow groups and rings; motives (14C15) Arithmetic properties of periodic points (37P35) Geometry over the field with one element (14A23)

Related Items (1)

Quantum statistical mechanics of the absolute Galois group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The class of the affine line is a zero divisor in the Grothendieck ring: an improvement
• The \(K\)-theory of assemblers
• On the arithmetic of the BC-system
• On \(K_{1}\) of an assembler
• Bost-Connes systems, categorification, quantum statistical mechanics, and Weil numbers
• The Burnside ring of profinite groups and the Witt vector construction
• The basic geometry of Witt vectors. I: The affine case
• The basic geometry of Witt vectors. II: Spaces
• Zeta-polynomials for modular form periods
• Lectures on algebraic categorification
• Commutative \(\Gamma \)-rings do not model all commutative ring spectra
• Absolute algebra and Segal's \(\gamma\)-rings: au dessous de \(\overline{\operatorname{Spec}(\mathbb{Z})}\)
• Cyclotomy and endomotives
• Fun with \(\mathbb F_1\)
• Grothendieck groups of Abelian group rings
• \(SK_ 1\) of an interesting principal ideal domain
• The existence of Morse-Smale diffeomorphisms
• Homology theory and dynamical systems
• \(q\)-deformations of statistical mechanical systems and motives over finite fields
• Categories and cohomology theories
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
• Derived \(\ell\)-adic zeta functions
• The annihilator of the Lefschetz motive
• Torified varieties and their geometries over \(\mathbb{F}_{1}\)
• Local zeta factors and geometries under SpecZ
• Moduli operad over $\mathbb F_1$
• Riemann hypothesis for period polynomials of modular forms
• Cyclotomy and analytic geometry over F_1
• Schemes over 𝔽₁and zeta functions
• The class of the affine line is a zero divisor in the Grothendieck ring
• Caractéristique d'Euler-Poincaré
• Smash products and Γ-spaces
• Stable homotopical algebra and Γ-spaces
• Symmetric spectra
• Equivariant analogues of the Euler characteristic and Macdonald type equations
• Linear recursive sequences andSpec(ℤ) over𝔽₁
• Higher-Order Spectra, Equivariant Hodge–Deligne Polynomials, and Macdonald-Type Equations
• Au-dessous de Specℤ
• The $K$-theory spectrum of varieties
• S-modules and symmetric spectra

This page was built for publication: Homotopy types and geometries below Spec(ℤ)