p-adic Arakelov theory

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Abstract

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
Volume111
Issue number2
DOIs
StatePublished - 1 Apr 2005

Keywords

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

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