Structural properties conjecture for character sheaves

Let $G$ be a connected unipotent algebraic group, let $e$ be a minimal idempotent of ${\mathscr D}_G(G)$, let ${\mathcal M}_e^{perv}$ be the full subcategory of perverse objects in $e{\mathscr D}_G(G)$, and let an ${\mathbb L}$-packet be the set of character sheaves belonging to $e$. Let $M_1,M_2$ be character sheaves. The structural properties conjecture. Character sheaves are irreducible perverse sheaves; $e{\mathscr D}_G(G)$ is generated as a triangulated subcategory by ${\mathcal M}_e^{perv}$;

$$\operatorname{Ext}^i_{{\mathscr D}_G(G)}(M_1,M_2)=0$$

for $i>0$; and all ${\mathbb L}$-packets for $G$ are finite. This conjecture is formulated together with the preceding conjectural existence of $n_e$.