Koszul duality, motivic Sullivan models, and Rational motivic delooping for mixed Tate curves

For the very special case of a mixed Tate curve X over an open integer scheme, we are in the process of showing that the map from augmentations of the motivic dga of X to torsors under unipotent pi_1 is bijective. Progress has been slowed by a necessary foundational step in which we upgrade Koszul duality for algebras in monoidal categories to include modules. While the general result is quite abstract, we are able to make a small piece of our result explicit in a calculation that also brings to our attention an interesting family of invariants of X; these, at least in my opinion, deserve to be studied. This is partly joint work with Tomer Schlank, partly joint with Asaf Horef, and partly incomplete.