A combinatorial Li-Yau inequality and rational points on curves

DOI10.1007/s00208-014-1067-xzbMath1341.11034arXiv1211.2681OpenAlexW2080713981MaRDI QIDQ2255277

Janne Kool, Gunther Cornelissen, Fumiharu Kato

Publication date: 9 February 2015

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2681

zbMATH Keywords

Drinfeld modular curvesgraphsgonalityfirst eigenvalueLaplacianhyperbolic volumeharmonic morphismnon-Archimedean fieldcongruence subgroups function fieldsrigid analyticstable gonality

Mathematics Subject Classification ID

Rational points (14G05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Arithmetic aspects of modular and Shimura varieties (11G18) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Drinfel'd modules; higher-dimensional motives, etc. (11G09) Special divisors on curves (gonality, Brill-Noether theory) (14H51) Rigid analytic geometry (14G22)

Related Items (19)

Problems hard for treewidth but easy for stable gonality ⋮ Multiplicity-free gonality on graphs ⋮ Gonality of abstract modular curves in positive characteristic ⋮ Treewidth is a lower bound on graph gonality ⋮ On metric graphs with prescribed gonality ⋮ Genus of abstract modular curves with level-\(\ell\) structures ⋮ Computing graph gonality is hard ⋮ Graphs of gonality three ⋮ Recognizing hyperelliptic graphs in polynomial time ⋮ Gonality of expander graphs ⋮ Constructing tree decompositions of graphs with bounded gonality ⋮ Constructing tree decompositions of graphs with bounded gonality ⋮ Stable divisorial gonality is in NP ⋮ Degeneration of Linear Series from the Tropical Point of View and Applications ⋮ Gonality Sequences of Graphs ⋮ On the scramble number of graphs ⋮ Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry ⋮ Lifting harmonic morphisms. I: Metrized complexes and Berkovich skeleta ⋮ Rational function semifields of tropical curves are finitely generated over the tropical semifield

Uses Software

• ComputeTW

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