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Syntomic regulators andp-adic integration I: Rigid syntomic regulators

Israel Journal of Mathematics volume 120, pages 291–334 (2000)Cite this article

Abstract

We construct a new version of syntomic cohomology, called rigid syntomic cohomology, for smooth schemes over the ring of integers of ap-adic field. This version is more refined than previous constructions and naturally maps to most of them. We construct regulators fromK-theory into rigid syntomic cohomology. We also define a “modified” syntomic cohomology, which is better behaved in explicit computations yet is isomorphic to rigid syntomic cohomology in most cases of interest.

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Author notes

  1. Amnon Besser

    Present address: Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, 84105, Be’er-Sheva, Israel

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  1. Department of Mathematical Sciences, University of Durham Science Laboratories, South Road, DH1 3LE, Durham, England

    Amnon Besser

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  1. Amnon Besser
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Correspondence to Amnon Besser.

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Besser, A. Syntomic regulators andp-adic integration I: Rigid syntomic regulators. Isr. J. Math. 120, 291–334 (2000). https://doi.org/10.1007/BF02834843

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Keywords

  • Spectral Sequence
  • Chern Class
  • Cohomology Theory
  • Chern Character
  • Admissible Covering