p-adic Arakelov theory

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13 Scopus citations


We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the metric on the determinant of its cohomology in the style of Faltings. We also prove analogues of the Adjunction formula and the Riemann-Roch formula.

Original languageEnglish
Pages (from-to)318-371
Number of pages54
JournalJournal of Number Theory
Issue number2
StatePublished - 1 Apr 2005


  • Arakelov theory
  • p-adic Green functions
  • p-adic height pairings
  • p-adic integration

ASJC Scopus subject areas

  • Algebra and Number Theory


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