Department of Mathematics2024-11-0920130022-314X10.1016/j.jnt.2012.10.0062-s2.0-84871408578http://dx.doi.org/10.1016/j.jnt.2012.10.006https://hdl.handle.net/20.500.14288/12294We 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].MathematicsJournal Article1096-1658314261300001Q38900