Multiple ζ-motives and moduli spaces M̄0,n

We give a natural construction of framed mixed Tate motives unramified over Z whose periods are the multiple ζ -values. Namely, for each convergent multiple ζ -value we define two boundary divisors A and B in the moduli space M̄0,n+3 of stable curves of genus zero. The corresponding multiple zeta-motive is the n th cohomology of the pair (M̄0,n+3-A,B) .