The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
Voevodsky, Triangulated categories of motives over a field, in: Cycles, transfers, and motivic homology theories, pp
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A construction of the polylogarithm motive
The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.