Elliptic associators

Understand

We construct a genus one analogue of the theory of associators and the Grothendieck-Teichmueller group.

• The analogue of the Galois action on the profinite braid groups is an action of the arithmetic fundamental group of a moduli space of elliptic curves on the profinite braid groups in genus one.
• This action factors through an explicit profinite group hat GT_ell, which admits an interpretation in terms of decorations of braided monoidal categories.
• We relate this group to its prounipotent group scheme version GT_ell(-).