Higher arithmetic intersection theory

DOI10.1016/j.aim.2019.02.003zbMath1439.14032arXiv1712.10150OpenAlexW2962744752MaRDI QIDQ1731573

Souvik Goswami, José Ignacio Burgos Gil

Publication date: 13 March 2019

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

Full work available at URL: https://arxiv.org/abs/1712.10150

zbMATH Keywords

Deligne cohomologyBeilinson regulatorarithmetic intersection theoryheight pairinghigher arithmetic Chow groups

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Heights (11G50) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (2)

Height pairing on higher cycles and mixed Hodge structures ⋮ Algebraic de Rham theory for the relative completion of 𝑆𝐿₂(ℤ)

Cites Work

• Higher arithmetic Chow groups
• Functional equations of the dilogarithm in motivic cohomology
• Algebraic cycles and higher K-theory
• Higher Bott-Chern forms and Beilinson's regulator
• Arithmetic intersection theory
• Biextensions and heights associated to curves of odd genus
• Hyperrésolutions cubiques et descente cohomologique. (La plupart des exposés d'un séminaire sur la théorie de Hodge-Deligne, Barcelona (Spain), 1982)
• Green forms and their product.
• Chow polylogarithms and regulators
• Higher arithmetic \(K\)-theory
• The Regulators of Beilinson and Borel
• On Goncharov’s Regulator and Higher Arithmetic Chow Groups
• Polylogarithms, regulators, and Arakelov motivic complexes
• COHOMOLOGICAL ARITHMETIC CHOW RINGS
• Additive higher Chow groups of schemes
• Mixed Hodge Structures
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