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Depth-graded motivic multiple zeta values · Around

2013

Depth-graded motivic multiple zeta values

Brown, Francis

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We study the depth filtration on multiple zeta values, the motivic Galois group of mixed Tate motives over $\mathbb{Z}$ and the Grothendieck-Teichm\"uller group, and its relation to modular forms.

Using period polynomials for cusp forms for $\mathrm{SL}_2(\mathbb{Z})$, we construct an explicit Lie algebra of solutions to the linearized double shuffle equations, which gives a conjectural description of all identities between multiple zeta values modulo $\zeta(2)$ and modulo lower depth.
We formulate a single conjecture about the homology of this Lie algebra which implies conjectures due to Broadhurst-Kreimer, Racinet, Zagier and Drinfeld on the structure of multiple zeta values and on the Grothendieck-Teichm\"uller Lie algebra.

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W. Kohnen, D. Zagier
1984
Earlier work this paper cites.
V. Drinfeld
1990
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Y. Ihara, N. Takao
1993
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D. Zagier
1993
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C. Weibel
1994
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D. Broadhurst, D. Kreimer
1997
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P. Cartier
2000
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A. B. Goncharov
2001
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Y. Ihara
2002
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G. Racinet
2002
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R. Sharifi
2002
Earlier work this paper cites.

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