Summary: We describe a torsor structure arising on the affine scheme defined by a system of \(\mathbb{Q}\)-algebraic relations between polyzetas at roots of unity, i.e., values of hyperlogarithmic functions on a fixed finite subgroup \(\Gamma\) of \(\mathbb{C}\). For \(\Gamma= \{1\}\) (polyzetas case), these relations are believed to span all the \(\mathbb{Q}\)-algebraic relations between those numbers. The formulas are derived from the action of \(\text{Gal} (\overline{\mathbb{Q}}/\mathbb{Q})\) on the projective line minus finitely many points.
See also the author’s follow-up article [ibid. 133, 11–16 (2001; Zbl 1033.11032)].