Deligne's algebraic definition conjecture for one-motives

Let $V$ be an arbitrary variety over an arbitrary field $k$, let $n$ be an integer, and let $\bar{k}$ be an algebraic closure of $k$. Write $T_{\ell}$ and $T_{DR}$ for the $\ell$-adic and de Rham realizations of a one-motive, respectively. Deligne's conjecture. There should be a one-motive $L^n(V/k)$ and homomorphisms

$$T_{\ell}(L^n(V/k))\to H^n(V\times\bar{k},\mathbb{Z}_{\ell}(1))/\operatorname{torsion},$$ $$T_{DR}(L^n(V/k))\to H^n_{DR}(V/k)$$

whose definitions are algebraic, canonical, and functorial in $V$ and $k$. Moreover,

$$L^n(V/\mathbb{C})\cong I^n(V)$$

canonically. This gives the conjectured purely algebraic definition of the one-motive attached to the cohomology of a variety; the source states that the result is proved in the article, while the candidate itself is marked with unknown resolution status.