On one example and one counterexample in counting rational points on graph hypersurfaces

DOI10.1007/s11005-011-0501-1zbMath1278.81089arXiv1006.3533OpenAlexW1988758826WikidataQ124847114 ScholiaQ124847114MaRDI QIDQ657631

Dzmitry Doryn

Publication date: 10 January 2012

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.3533

zbMATH Keywords

Feynman graphgraph hypersurfaceKontsevich conjecturenumber of \({\mathbb F_q}\)-rational points

Mathematics Subject Classification ID

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Varieties over finite and local fields (11G25)

Related Items (10)

On \(c_2\) invariants of some 4-regular Feynman graphs ⋮ A result on the invariant for powers of primes ⋮ SOME RESULTS ON AN ALGEBRO-GEOMETRIC CONDITION ON GRAPHS ⋮ A \(K3\) in \(\phi^{4}\) ⋮ Feynman integrals and motives of configuration spaces ⋮ Matroid connectivity and singularities of configuration hypersurfaces ⋮ Potts models with magnetic field: arithmetic, geometry, and computation ⋮ Feynman quadrics-motive of the massive sunset graph ⋮ Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications ⋮ Motives of graph hypersurfaces with torus operations

Cites Work

• Quantum field theory over \(\mathbb F_q\)
• Cohomology of graph hypersurfaces associated to certain Feynman graphs
• On motives associated to graph polynomials
• Quantum periods: a census of \(\phi^4\)-transcendentals
• Counting points on varieties over finite fields related to a conjecture of Kontsevich
• Matroids, motives, and a conjecture of Kontsevich.
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Motives associated to sums of graphs
• Knots and Numbers in ϕ⁴ Theory to 7 Loops and Beyond

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