3 problems

Good-characteristic parity conjecture. If $p$ is a good prime for ${\mathbf G}$, then the standard sheaves with coefficients in a field of characteristic $p$ are $*$-parity.

Parity induction conjecture. The complex

Let $\Gamma$ be a quiver and let $\mathbf{k}$ be a field. Call $\Gamma$ $\mathbf{k}$-even if the complexes $\pi_{y*}\underline{\mathbf{k}}_{\widetilde{F}_{y}}$ are even for every…