On the Goncharov depth conjecture and polylogarithms of depth two

• Steven Charlton ^[1] ; Herbert Gangl ^[2] ; Danylo Radchenko ^[4] ; Daniil Rudenko ^[3]
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  2. [2] Durham University

     Durham University

     Reino Unido

     
  3. [3] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
  4. [4] Laboratoire Paul Painlevé, Université de Lille, France

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 2, 2024, 7 págs.
• Idioma: inglés
• DOI: 10.1007/s00029-024-00918-6
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• Resumen

  • We prove the surjectivity part of Goncharov’s depth conjecture over a quadratically closed field. We also show that the depth conjecture implies that multiple polylogarithms of depth d and weight n can be expressed via a single function Lin−d+1,1,...,1(a1, a2,..., ad ), and we prove this latter statement for d = 2

• Referencias bibliográficas
  • Goncharov, A.B.: Hyperlogarithms, mixed Tate motives and multiple ζ -numbers (1993). Preprint MSRI 058-93
  • Goncharov, A.B.: Geometry of configurations, polylogarithms, and motivic cohomology. Adv. Math. 114(2), 197–318 (1995)
  • Goncharov, A.B.: Multiple polylogarithms and mixed Tate motives (2001). arXiv:math/0103059
  • Matveiakin, A., Rudenko, D.: Cluster polylogarithms I: quadrangular polylogarithms (2022). arXiv:2208.01564