The cyclotomic double shuffle torsor in terms of Betti and de Rham coproducts

Abstract

We prove a cyclotomic generalization of Enriquez and Furusho's result stating that the scheme DMR× of double shuffle and regularization relations between multiple zeta values arising from Racinet's formalism is a torsor of isomorphisms between “Betti” and “de Rham” objects. After reviewing the “de Rham” objects arising from a crossed product interpretation of Racinet's formalism, we construct the “Betti” objects based on the orbifold fundamental group of the quotient (C×∖μN)/μN with μN being the group of Nth roots of unity for N≥1. We then show that DMR× is a subtorsor of stabilizer schemes relating “Betti” and “de Rham” coproducts.