8 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.

Let $G$ be the reductive group in the setup, let $C\subset\mathcal{N}$ be a nilpotent orbit, and let $x_C$ be the corresponding element whose reductive centralizer is…

Parity induction conjecture. The complex

Treumann's conjecture. The image under $\mathbf{Psm}$ of a $\varpi$-equivariant perverse sheaf on $X$ is a direct sum of shifts of projections of trivially equivariant perverse she…

Tilting conjecture. In arbitrary characteristic, for every dominant weight $\lambda\in\Lambda^+$, the perverse sheaf

Let $G$ be a connected complex reductive group with Langlands dual group $G^\vee$, and let $\mathcal{G}r$ be its affine Grassmannian. A prime $p$ is a JMW prime for $G^\vee$ if it…

Let $V$ be a finite dimensional $I$-graded $\mathbb{C}$-vector space, let $\Lambda_V$ be the set of $G_V$-orbits in $E_V$, and let $\lambda\in\Lambda_V$. Write…

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…