Depth-graded motivic multiple zeta values

Abstract

We study the depth filtration on multiple zeta values, the motivic Galois group of mixed Tate motives over $\mathbb{Z}$ and 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-Kreimer, Racinet, Zagier and Drinfeld on the structure of multiple zeta values and on the Grothendieck-Teichmüller Lie algebra.

arXiv commentRewritten introduction, added brief section explaining the depth-spectral sequence, and made a few proofs more user-friendly by adding some more details