5. Parity Sheaves and Torsion in IC Sheaves

Problem 5.1.
[Achar–Williamson] For which primes $p$ is it true that all indecomposable $B$constructible parity $\F_p$ sheaves on $G/B$ are perverse?
 Same question for $I$constructible parity $\F_p$sheaves on $Gr$.
(Expect this to be true for large $p$.) 
Problem 5.2.
[Mautner] For which primes $p$ do the IC sheaves on $\operatorname{Perv}_I(Gr, \Z_p)$ have torsionfree stalks?
(Related to Problem 10.1 part 2, and to Extvanishing between reduced standard and costandard modules.) 
Problem 5.3.
[Williamson] Give nontrivial sufficient conditions for indecomposable parity sheaves on $G/B$ or $Gr$ or $Fl$ to be simple perverse sheaves. 
Problem 5.4.
[Achar] Is there a faster algorithm to compute indecomposable parity sheaves on $\operatorname{Perv}_{\mathrm{sph}}(Gr, \F_p)$ than by computing the $p$canonical basis?
(Motivated by A. Broer’s algorithm in characteristic 0.)
Cite this as: AimPL: Sheaves and modular representations of reductive groups, available at http://aimpl.org/sheavemodular.