Boundary-factorization conjecture for motivic groups KZ,nK_{\mathbb{Z},n}

Let DM0,n1×M0,n2D\simeq\mathcal{M}_{0,n_1}\times\mathcal{M}_{0,n_2} be a codimension-one boundary component, and let KZ,n1,n2K^{\bullet}_{\mathbb{Z},n_1,n_2} denote the geometric derived group associated with this boundary stratum. Boundary-factorization conjecture. The induced morphism

KZ,n1,n2pn1,n2KZ,n1×KZ,n2K^{\bullet}_{\mathbb{Z},n_1,n_2}\xrightarrow[p_{n_1,n_2}]{}K^{\bullet}_{\mathbb{Z},n_1}\times K^{\bullet}_{\mathbb{Z},n_2}

is an isomorphism. If true, this would reduce the relevant boundary construction to the two factors and support defining GTZ(S)GT^{\bullet}_{\mathbb{Z}}(S) using only automorphisms of the groups KnK^{\bullet}_n; the stronger analogous assertion for the full groups GZ,nG^{\bullet}_{\mathbb{Z},n} is stated separately in the source.

Sources & referencesView supporting material

Primary source

Ismael Soudères, “A Motivic Grothendieck-Teichmüller Group”, arXiv:1502.05640 (2015).

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