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On \(l\)-adic iterated integrals. III: Galois actions on fundamental groups. (English) Zbl 1134.11331
Summary: We continue to study \(l\)-adic iterated integrals introduced in the first part [Nagoya Math. J. 176, 113–158 (2004; Zbl 1160.11333)]. We calculate explicitly \(l\)-adic logarithm and \(l\)-adic polylogarithms. Next we use these results to study Galois representations on the fundamental group of \(\mathbb P^1_{\overline{\mathbb Q(\mu_n)}}\setminus\{0,\mu_n,\infty\}\).
Fro Part II, see Nagoya Math. J. 177, 117–153 (2005; Zbl 1161.11363).

MSC:
11G55 Polylogarithms and relations with \(K\)-theory
19D45 Higher symbols, Milnor \(K\)-theory
19D55 \(K\)-theory and homology; cyclic homology and cohomology
19E20 Relations of \(K\)-theory with cohomology theories
19F27 Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)
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