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arXiv · 1208.0516

The syntomic regulator for $K_4$ of curves

Amnon Besser·Rob de Jeu
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Abstract

Let $C$ be a curve defined over a discrete valuation field of characteristic zero where the residue field has positive characteristic. Assuming that $C$ has good reduction over the residue field, we compute the syntomic regulator on a certain part of $K_4^[(3)}(C)$. 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 $K_4^[(3)}(F)$ for the function field $F$ of $C$. The result can be expressed in terms of $p$-adic polylogarithms and Coleman integration, or by using a trilinear map ("triple index") on certain functions.

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Amnon Besser, Rob de Jeu. 2012-08-02. The syntomic regulator for $K_4$ of curves. https://arxiv.org/abs/1208.0516

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