Hodge realizations of 1-motives and the derived Albanese

摘要

We prove that the embedding of the derived category of 1-motives up to isogeny into the triangulated category of effective Voevodsky motives, as well as its left adjoint functor LAlb ?, commute with the Hodge realization. This result yields a new proof of the rational form of Deligne's conjecture on 1-motives.