Mixed Tate motives over dual numbers conjecture

Let Fε=F[ε]/(ε2)F_{\varepsilon}=F[\varepsilon]/(\varepsilon^2), and let Q(Fε){\cal Q}_{\bullet}(F_{\varepsilon}) be the Lie coalgebra combining the non-Euclidean and Euclidean scissor-congruence coalgebras. A finite-dimensional graded comodule means a finite-dimensional object equipped with the compatible graded coaction of this Lie coalgebra. Mixed Tate motives over dual numbers conjecture. The category of finite-dimensional graded comodules over Q(Fε){\cal Q}_{\bullet}(F_{\varepsilon}) is naturally equivalent to a subcategory of the category of mixed Tate motives over FεF_{\varepsilon}. This proposes a motivic interpretation of the scissor-congruence coalgebra for dual numbers, relating its comodules to mixed Tate motives while asserting only an embedding into the full motivic category.

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Primary source

A. B. Goncharov, “Euclidean scissor congruence groups and mixed Tate motives over dual numbers”, arXiv:math/0401354 (2004).

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