A geometric interpretation of double shuffle relations between multiple zeta values - B.Enriquez

Mar 23, 2023  ·   From Paris France  ·   Event ``Arithmetic & Homotopic Galois Theory 2023''

Abstract

The ``associator'' and ``double shuffle'' relations between multiple zeta values give rise to two torsors (due respectively to Drinfeld and Racinet), which both contain the torsor of mixed Tate motives over \(\mathbb Z\).
Following ideas of Deligne and Terasoma, we propose a geometric interpretation of the ``double shuffle'' torsor. This is applied to the solution of two problems: (a) making explicit the bitorsor structure underlying the double shuffle torsor; (b) proving (independently of Furusho's 2011 proof) the inclusion of the associator torsor in the double shuffle one.