Drinfelʼd–Ihara relations for p-adic multi-zeta values

Abstract

We prove that the p-adic multi-zeta values satisfy the Drinfel'd-Ihara relations in Grothendieck-Teichmuller theory (Drinfel'd (1991) [10], Ihara (1991) [21]). This requires a detailed study of the crystalline theory of tangential basepoints in the higher dimensional case and Coleman integrals (Coleman (1982) [5]) as they relate to the frobenius invariant path of Vologodsky (2003) [31]. The main result (Theorem 1.8.1) is used in Furusho (2007) [14, pp. 1133-1135].