## Abstract

We define complexes analogous to Goncharov's complexes for the K-theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K-theory, there is a map from the cohomology of those complexes to the K-theory of the ring under consideration. In case the ring is a localization of the ring of integers in a number field, there are no assumptions necessary. We compute the composition of our map to the K-theory with the syntomic regulator. The result can be described in terms of a p-adic polylogarithm. Finally, we apply our theory in order to compute the regulator to syntomic cohomology on Beilinson's cyclotomic elements. The result is again given by the p-adic polylogarithm. This last result is related to one by Somekawa and generalizes work by Gros.

Original language | English |
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Pages (from-to) | 867-924 |

Number of pages | 58 |

Journal | Annales Scientifiques de l'Ecole Normale Superieure |

Volume | 36 |

Issue number | 6 |

DOIs | |

State | Published - 1 Nov 2003 |