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1 results

  • Multiple $\zeta$-motives and moduli spaces $\overline{\mathcal{M}}_{0,n}$

  • A. B. Goncharov, Yu. I. Manin
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-14
    Print publication:
    January 2004
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  • We give a natural construction of framed mixed Tate motives unramified over $\mathbb{Z}$ whose periods are the multiple $\zeta$-values. Namely, for each convergent multiple $\zeta$-value we define two boundary divisors A and B in the moduli space $\overline{\mathcal{M}}_{0,n+3}$ of stable curves of genus zero. The corresponding multiple zeta-motive is the nth cohomology of the pair $(\overline{\mathcal{M}}_{0,n+3}-A,B)$.