10 August 2018
9 August 2018
7 August 2018
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 ℚ, commute with the Hodge realization. This result yields a new proof of the rational form of Deligne's conjecture on 1-motives.
We show how the notion of the transcendence degree of a zero-cycle on a smooth projective variety X is related to the structure of the motive M(X). This can be of particular interest in the context of Bloch's conjecture, especially for Godeaux surfaces, when the surface is given as a finite quotient of a suitable quintic in P^3.
The purpose of this paper is to construct non-trivial elements in the Abel-Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical invariants at points with different transcendence degrees over a subfield in C.