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The Syntomic Regulator for K2 of Curves with Arbitrary Reduction

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Part of the Progress in Mathematics book series (PM,volume 338)

Abstract

We give a formula for the syntomic regulator on K2 of a proper curve X over a p-adic field K. This generalizes the results of [Bes00c] where the curve was assumed to have good reduction. The formula is essentially the same with Coleman integration replaced by by Vologodsky integration.

Keywords

  • p-adic cohomology
  • syntomic cohomology
  • regulators
  • algebraic Ktheory
  • p-adic integration

Mathematics Subject Classification

  • Primary: 19F27
  • 11S80
  • Secondary: 11G20
  • 11G20

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  • DOI: 10.1007/978-3-030-65203-6_3
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Besser, A. (2021). The Syntomic Regulator for K2 of Curves with Arbitrary Reduction. In: Charollois, P., Freixas i Montplet, G., Maillot, V. (eds) Arithmetic L-Functions and Differential Geometric Methods . Progress in Mathematics, vol 338. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-65203-6_3

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