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Kato, Kazuya [Author] ; Abbes, Ahmed (Organization) [Other]; Hu, Yongquan (Organization) [Other]; Orgogozo, Fabrice (Organization) [Other]; Saito, Takeshi (Organization) [Other]; Shiho, Atsushi (Organization) [Other]; Tian, Ye (Organization) [Other]; Tsuji, Takeshi (Organization) [Other]; Zheng, Weizhe (Organization) [Other]

Height of motives

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  • Media type: E-Book; Video
  • Title: Height of motives
  • Contributor: Kato, Kazuya [Author]; Abbes, Ahmed (Organization) [Other]; Hu, Yongquan (Organization) [Other]; Orgogozo, Fabrice (Organization) [Other]; Saito, Takeshi (Organization) [Other]; Shiho, Atsushi (Organization) [Other]; Tian, Ye (Organization) [Other]; Tsuji, Takeshi (Organization) [Other]; Zheng, Weizhe (Organization) [Other]
  • Published: [Erscheinungsort nicht ermittelbar]: Institut des Hautes Études Scientifiques (IHÉS), 2013
  • Published in: Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo ; (Jan. 2013)
  • Extent: 1 Online-Ressource (588 MB, 01:13:38:01)
  • Language: English
  • DOI: 10.5446/20484
  • Identifier:
  • Origination:
  • Footnote: Audiovisuelles Material
  • Description: The height of a rational number a/b (a, b integers which are coprime) is defined as max(|a|, |b|). A rational number with small (resp. big) height is a simple (resp. complicated) number. Though the notion of height is so naive, height has played fundamental roles in number theory. There are important variants of this notion. In 1983, when Faltings proved Mordell conjecture, Faltings first proved Tate conjecture for abelian variaties by defining heights of abelian varieties, and then he deduced Mordell conjecture from the latter conjecture. I will explain that his height of an abelian variety is generalized to the height of a motive. This generalization of height is related to open problems in number theory. If we can prove finiteness of the number of motives of bounded heights, we can prove important conjectures in number theory such as general Tate conjecture and Mordell-Weil type conjectures in many cases
  • Access State: Open Access
  • Rights information: Attribution - Non Commercial (CC BY-NC)