I have asked this question on Math StackExchange, but have not got any reply.

In section 1.7 of Deligne's paper "Valeurs de fonctions L et périodes d'intégrales", which has an English translation (pdf here), 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, could anyone explain the definition?

Also in this section, the author defines subspaces, \begin{equation} H^+_{DR}(M):=H_{DR}(M)/F^-,~~H^-_{DR}(M):=H_{DR}(M)/F^+ \end{equation} and it has said later in the same 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 carefully?