## Abstract

Let C be a curve defined over a complete discrete valuation subfield of Cp. Assuming that C has good reduction over the residue field, we compute the syntomic regulator on a certain part of K^{(3)} _{4} (C). The result can be expressed in terms of p-adic polylogarithms and Coleman integration. We also compute the syntomic regulator on a certain part of K^{(3)} _{4} (F) or the function field F of C. The result can be expressed in terms of p-adic polylogarithms and Coleman integration, or byusing a trilinear map ("triple index") on certain functions.

Original language | English |
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Pages (from-to) | 305-380 |

Number of pages | 76 |

Journal | Pacific Journal of Mathematics |

Volume | 260 |

Issue number | 2 |

DOIs | |

State | Published - 1 Dec 2012 |

## Keywords

- Algebraic K-theory
- Syntomic regulator
- p-adic polylogarithm

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