On the p-adic beilinson conjecture for number fields

A. Besser, P. Buckingham, R. de Jeu, X. F. Roblot

Research output: Contribution to journalArticlepeer-review

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Abstract

We formulate a conjectural p-adic analogue of Borel's theorem relating regulators for higher K-groups of number fields to special values of the corresponding ζ-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of the conjectures are proved when the number field (or Artin motive) is Abelian over the rationals, and all conjectures are verified numerically in various other cases.

Original languageEnglish
Pages (from-to)375-434
Number of pages60
JournalPure and Applied Mathematics Quarterly
Volume5
Issue number1
DOIs
StatePublished - 1 Jan 2009

Keywords

  • Artin motive
  • Beilinson conjecture
  • Borel's theorem
  • Number field
  • P-adic l-function
  • Syntomic regulator

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