Non-abelian unipotent periods and monodromy of iterated integrals. (2003) 2(1),

Zdzislaw, Jozef Wojtkowiak (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

In this note we are studying the Lie algebras associated to non-abelian unipotent periods on P1ℚ(μn)∖{0,μn,∞}. Let n be a prime number. We assume that for any m≥1 the numbers Lim+1(ξkn) for 1≤k≤(n−1)/2 are linearly independent over ℚ in ℂ/(2π\ri)m+1ℚ. Let S={k1,⋯,kq} be a subset of {1,…,p−1} such that if k∈S, then p−k∈S and (S+S)∩S=∅ (the sum of two elements of S is calculated Modp). Then we show that in the Lie algebra associated to non-abelian unipotent periods on P1ℚ(μn)∖{0,μn,∞} there are derivations Dk1m+1,…,Dkqm+1 in each degree m+1 and these derivations are free generators of a free Lie subalgebra of this Lie algebra.

Domaines: Théorie des nombres [math.NT]

Zdzislaw, Jozef Wojtkowiak. Non-abelian unipotent periods and monodromy of iterated integrals. (2003) 2(1), . Journal of the Institute of Mathematics of Jussieu, 2003. ⟨hal-01293667⟩