The syntomic regulator for K₄ of curves

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.