3 problems

Humphreys–Verma conjecture on lifting projective $G_r$ -modules
arXiv@arxiv
Humphreys–Verma conjecture. For $\lambda\in X_r$ , the $G_r$ -module structure on $Q_r(\lambda)$ can be lifted to $G$ .
Conjectureopenalgebraic-groups frobenius-kernels representation-theory
0
Conjecture that Frobenius-kernel projective covers are rational modules
arXiv@arxiv
Projective-cover module conjecture. The $G_r$ -projective covers of irreducible modules are $G$ -modules.
Conjectureopenalgebraic-groups frobenius-kernels modular-representation-theory
0
Lifting conjecture for projective indecomposable modules of Frobenius kernels
arXiv@arxiv
Let $G$ be an algebraic group, let $G_r$ be its $r$ -th Frobenius kernel, and let $P$ be a projective indecomposable $G_r$ -module. Lifting conjecture. The $G_r$ -action on $P$ should…
Conjectureopenalgebraic-groups frobenius-kernels representation-theory
0

Humphreys–Verma conjecture on lifting projective GrG_rGr​-modules