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

Published online by Cambridge University Press:  04 December 2007

A. B. Goncharov  and
Yu. I. Manin
A. B. Goncharov
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912, USAsasha@math.brown.edu
Yu. I. Manin
Affiliation:
Max–Planck–Institut für Mathematik, Vivatsgasse 7, Bonn, Germanymanin@mpim-bonn.mpg.de
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Abstract

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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 $(\overline{\mathcal{M}}_{0,n+3}-A,B)$.

Keywords

multiple $\zeta$-valuesmoduli spacesmixed Tate motives11G5511F6711R3220F34
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 1 , January 2004 , pp. 1 - 14
Copyright
Foundation Compositio Mathematica 2004