In section 1.7 of Deligne's paper Valeur de Fonctions L et periodes d'integrales, which has a translation
http://www.math.tifr.res.in/~eghate/Deligne.pdf
there are two subspaces $F^+$ and $F^-$ appearing in the Hodge filtration of the de Rham realisation $H_{DR}(M)$ of a pure motive $M$. However these two subspaces haven't been defined, anyone who could explain the definition?
In this section, the author defines \begin{equation} H^+_{DR}(M):=H_{DR}(M)/F^-,~~H^-_{DR}(M):=H_{DR}(M)/F^+ \end{equation} and it has said later in this section that the dual of $H^+_{DR}(M)$ (resp. $H^-_{DR}(M)$) is the subspace $F^+$ (resp. $F^-$) of $H_{DR}(M^\vee)$, where $M^\vee$ is the dual motive of $M$. I don't understand this statement, and could anyone explain it to me?
Edit, after some time, I have also asked this question on MO