Curves, dynamical systems, and weighted point counting

DOI10.1073/pnas.1217710110zbMath1295.11124arXiv1209.5782OpenAlexW1999986065WikidataQ36932432 ScholiaQ36932432MaRDI QIDQ5170969

Gunther Cornelissen

Publication date: 25 July 2014

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.5782

zbMATH Keywords

Jacobianzeta function\(\ell\)-adic sheavesDirichlet \(L\)-seriesDirichlet characterFrobenius twistprojective irreducible curveweighted point counting

Mathematics Subject Classification ID

Class field theory (11R37) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Zeta and (L)-functions in characteristic (p) (11M38) Dynamical systems over finite ground fields (37P25)

Related Items (7)

Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions ⋮ Isomorphism invariants for multivariable \(C^\ast\)-dynamics ⋮ Pair arithmetical equivalence for quadratic fields ⋮ Reconstructing global fields from dynamics in the abelianized Galois group ⋮ Semicrossed products of operator algebras by semigroups ⋮ Characterization of global fields by Dirichlet \(L\)-series ⋮ KMS states on Pimsner algebras associated with \(C^\ast\)-dynamical systems

Cites Work

• Arithmetic equivalence for function fields, the Goss zeta function and a generalisation
• On Bost-Connes type systems for number fields
• Isomorphisms of Galois groups of algebraic function fields
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
• Constructing distinct curves with isomorphic Jacobians
• Trivial \(L\)-functions for the rational function field
• A Torelli theorem for curves over finite fields
• Quantum statistical mechanics over function fields
• Endomorphisms of Abelian varieties over finite fields

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