83 problems

Let $G$ be a group, let $\Bbbk$ be a field of characteristic $l$, and let $(C,\mathcal{E})\in\mathscr{I}(G)$ be a $0$-cuspidal pair. A prime $l$ is rather good for $G$ if it is goo…

For a simple perverse sheaf $\mathcal{S}$ in the block $\mathcal{D}_{G_{\underline0}}(\mathfrak{g}^{nil}_{\underline\eta})_{\xi}$, define … By the preceding corollary, this is a mo…

Irreducibility conjecture. Moreover, if ${\mathcal S}$ is irreducible, then so is $\Eis({\mathcal S})$.

Let $f:Y'\to Y”$ be a proper map between schemes over an algebraically closed field, and let $\CF$ be an irreducible $\ell$-adic perverse sheaf on $Y'$ obtained by the six operatio…

Let $\overline{A}$ and $\overline{X}$ be quasi-projective varieties over $\mathbb C$, with $\overline{A}$ smooth, and let $\overline{f}:\overline{A}\to\overline{X}$ be a projective…

Let $X$ be the curve and $G$ the reductive group of the paper. Let $E$ be a $\check{G}$-local system on $X$, and put $W=V^{\gamma}_E$. Assume that $W$ is irreducible and that whene…

Let ${\mathcal{P}}$ be the category of semisimple perverse sheaves on ${\mathfrak{T}(\mathbf{d})}'$, let $\mathcal{D}:{\mathcal{P}}\to{\mathcal{P}}$ be Verdier duality, and let…

Let ${\mathcal{P}}$ be the category of semisimple perverse sheaves on ${\mathfrak{T}(\mathbf{d})}'$ constructible with respect to the stratification by the…

Let $X$ be a stratified space with stratification ${\cal S}$, let ${\cal P}(X,{\cal S})$ denote MacPherson's category of perverse sheaves, and let $D^b_{\cal S}(X)$ denote the boun…

Let $G$ be a semisimple group, let $I\subset L^+G$ be an Iwahori subgroup, and let $Gr$ be the affine Grassmannian. Let $P_I(Gr)$ be the category of $I$-equivariant perverse sheave…

Let $G$ be a semisimple group, let $G^\lor$ be its Langlands dual, and let $X$ be the underlying curve. Let $\Lambda$ be the set of isomorphism classes of pairs $(P,\chi)$, where…

Toda's chi-independence conjecture. For any $\gamma\in B_S(\alpha)$, the invariant $\Phi(\alpha+n\delta)$ is independent of $n\in\mathbb{Z}$.

Let $(X,\mathcal{L},\alpha)$ be an oriented $-1$-shifted contact derived stack over $\mathbb{K}$, and let $\varphi\colon L\to X$ be a proper oriented Legendrian. Write … for the re…

Let $\mathrm{X}$ be a holomorphic symplectic manifold, and let $\mathscr{D}_\mathrm{L}$ and $\mathscr{D}_\mathrm{M}$ be quantised orientation modules associated to Lagrangian subma…

Let $\pi:\mathcal X\to\Delta$ be a projective conifold degeneration, and let $\mathcal P$ be the corrected perverse object constructed from nearby and vanishing cycles. Suppose the…

Let $\pi:\mathcal X\to\Delta$ be a projective conifold degeneration, and let $\mathcal P$ be the corrected perverse object constructed from nearby and vanishing cycles. A mixed-Hod…

Let $H$ be a $p$-adic reductive group, let $\lambda^{\mathbb{Q}_p}$ be an infinitesimal character, and let $\xi=(C,\mathcal{V})$ and $\xi'$ be parameters indexing the corresponding…

Finkelberg–Mirković conjecture. There exists an equivalence

Let $G$ be a reductive group with Langlands parameter $\varphi$ satisfying $I_F\subseteq\ker\varphi$ and … where $\lambda$ is dominant integral in the fundamental positive chamber.…

Let $G$ be a reductive group, let $\xi=(M,\lambda,L,\mathcal{O},\mathcal{L})$ be a polar-cuspidal datum for $G$, and let $\mathbf{Q}\subset LM$ be a parahoric subgroup containing…

Let $\check G$ be a connected reductive algebraic group over $F=\mathbb{Q}_p$, let $G$ be its Langlands dual group, and let $\Lambda:W_F\to{}^L\check G$ be an infinitesimal charact…

Let $G=\mathrm{SL}_n$, let $\overline{\mathrm{Bun}}_{B^-}$ be the compactification of the moduli stack of $B^-$-bundles, and let $\mathrm{IC}_{\overline{\mathrm{Bun}}_{B^-}}$ denot…

Let $G$ be a reductive group, let $\overline{\mathrm{Bun}}_{N^-}$ be the compactification used in the paper, and let $\mathrm{IC}_{\overline{\mathrm{Bun}}_{N^-}}$ denote its inters…

Let $\ell\geq h$. The category $\mathrm{Perv}_{I_\mathrm{u}}(\mathcal{F}l^{\frac{\infty}{2}})$ has simple objects $\mathrm{IC}_x^{\frac{\infty}{2}}$, standard objects…

Enriques perverse Hodge generating-series conjecture. The perverse Hodge numbers satisfy the displayed generating-series identity involving the theta functions, eta functions, and…