The Weil Proof and the Geometry of the Adelès Class Space

DOI10.1007/978-0-8176-4745-2_8zbMath1208.11108arXivmath/0703392OpenAlexW1661815629WikidataQ60020407 ScholiaQ60020407MaRDI QIDQ4929760

Matilde Marcolli, Caterina Consani, Alain Connes

Publication date: 24 September 2010

Published in: Progress in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703392

zbMATH Keywords

noncommutative geometryRiemann hypothesisadèles

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Noncommutative geometry (à la Connes) (58B34) Relations with noncommutative geometry (11M55)

Related Items

The Connes-Consani plane connection ⋮ Quantum statistical mechanics over function fields ⋮ Axiomatics as a Functional Strategy for Complex Proofs: The Case of Riemann Hypothesis ⋮ Toward a Galois theory of the integers over the sphere spectrum ⋮ Noncommutative geometry and motives: the thermodynamics of endomotives ⋮ The BC-system and \(L\)-functions ⋮ The hyperring of adèle classes ⋮ Probabilistic trace and Poisson summation formulae on locally compact abelian groups ⋮ Bost-Connes systems, categorification, quantum statistical mechanics, and Weil numbers ⋮ On \(p\)-adic mathematical physics ⋮ Cyclotomy and endomotives ⋮ Spectral symmetries of zeta functions ⋮ The operator algebra content of the Ramanujan-Petersson problem ⋮ Fun with \(\mathbb F_1\)

Cites Work

• On a representation of the idele class group related to primes and zeros of \(L\)-functions
• Duality for crossed products and the structure of von Neumann algebras of type III
• KMS states and complex multiplication
• On motives associated to graph polynomials
• Bost-Connes type systems for function fields
• The longitudinal index theorem for foliations
• The flow of weights on factors of type III
• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
• Basic number theory.
• 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
• A Lefschetz fixed point formula for elliptic complexes. I
• Tomita's theory of modular Hilbert algebras and its applications
• Théorie de Hodge. III
• Sur la théorie du corps de classes
• Multiple $\zeta$-motives and moduli spaces $\overline{\mathcal{M}}_{0,n}$
• From Endomorphisms to Automorphisms and Back: Dilations and Full Corners
• Une classification des facteurs de type ${\rm III}$
• On the Riemann Hypothesis in Function-Fields
• Lectures on spectral theory of elliptic operators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item