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Depth-graded motivic multiple zeta values
- Part of
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- Journal:
- Compositio Mathematica / Volume 157 / Issue 3 / March 2021
- Published online by Cambridge University Press:
- 22 March 2021, pp. 529-572
- Print publication:
- March 2021
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- Article
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We study the depth filtration on multiple zeta values, on the motivic Galois group of mixed Tate motives over
$\mathbb {Z}$ and on the Grothendieck–Teichmüller 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 and Kreimer, Racinet, Zagier, and Drinfeld on the structure of multiple zeta values and on the Grothendieck–Teichmüller Lie algebra.
