Hodge realizations of 1-motives and the derived Albanese

We prove that the embedding of the derived category of 1-motives into the triangulated category of effective Voevodsky motives, as well as its left adjoint functor $LAlb$, commute with the Hodge realization.

💡 Research Summary

The paper investigates the interaction between the derived category of 1‑motives and Voevodsky’s triangulated category of effective geometric motives, focusing on the behavior of these categories under the Hodge realization functor. After recalling the construction of the abelian category of 1‑motives (objects of the form (