In Hanamura's paper Mixed Motives and Algebraic Cycles III


<http://intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0001/MRL-1999-0006-0001-a005.pdf>


He proved that if assume Grothendieck's standard conjecture, Murre's conjecture and vanishing conjecture, there is a $t$ structure on Voevodsky's category of mixed motives $\textbf{DM}\_{\text{gm}}(k,\mathbb{Q})$, whose heart is an abelian category $\text{MM}(k)$. Each of Betti, etale or de Rham cohomology (realisation) functor 
\begin{equation}
\mathbb{R}\Gamma:\textbf{DM}\_{\text{gm}}(k,\mathbb{Q}) \rightarrow D^b(\Lambda-\text{Vec})
\end{equation}
(for suitable $\Lambda$) is a $t$-exact functor with respect to this $t$ structure and the natural $t$ structure on $D^b(\Lambda-\text{Vec})$. I have several questions,


1, Is the vanishing conjecture Hanamura assumed in his paper stronger or equivalent to the Beilinson-Soule vanishing conjecture about field $k$?


2, Is $\textbf{DM}\_{\text{gm}}(k,\mathbb{Q})$ the bounded derived category of $\text{MM}(k)$?, i.e. $\textbf{DM}\_{\text{gm}}(k,\mathbb{Q})=D^b(\text{MM}(k))$? Has this been proved in Hanamura's paper or is it still only a conjecture (even with several conjectures assumed)?


3, Let the restriction of $\mathbb{R}\Gamma$ to $\text{MM}(k)$ be
\begin{equation}
\Gamma:\text{MM}(k) \rightarrow \Lambda-\text{Vec}
\end{equation}
Since $\mathbb{R}\Gamma$ is $t$ exact, then $\Gamma$ is an exact functor, therefore the derived functor of $\Gamma$ is well defined.
\begin{equation}
D\Gamma:D^b(\text{MM}(k)) \rightarrow D^b(\Lambda-\text{Vec})
\end{equation}
If 2 is true, if $D\Gamma$ the same as (or equivalent to $\mathbb{R}\Gamma$)? 
Any references or comments will be sincerely appreciated!



Clarification on Hanamura's work on $t$ structure of triangulated category of mixed motives
1) I believe that the (Murre's) vanishing needed for Hanamura's argument is stronger than the BS conjecture.


2) There are certain standard conditions ensuring that a triangulated category is equivalent to the derived category of the heart of a t-structure on it. Yet I don't known much about them and they were not treated by Hanamura; thus it is not clear which conjectures are needed to answer your question.


3) This should be easy since the category of vector spaces is semi-simple.


