19 problems

Local constancy conjecture. If $U$ is contractible, then the restriction functor $i_u^*$ is an equivalence. This is the fiberwise formulation of local constancy for the automorphic…

Kazhdan–Lusztig singular-support conjecture. The singular support of $\sideset{^{\pi}}{_{X_w}}{\Bbb C}$ is irreducible.

Let $\pi:\mathfrak{X}\to S$ be the family of curves in the paper, let $\operatorname{Bun}_G(\pi_U)$ be the moduli stack of $G$-bundles on the base-changed family over a contractibl…

Let $g:\mathcal Z\to\mathcal Y$ be a quasi-smooth map, let $\phi$ be an endomorphism of $\mathcal Y$ lifting to $\mathcal Z$, and let $\mathcal N$ be a conical singular-support con…

Let $Q$ be a finite quiver without loops, let $E$ be a variety of representations of $Q$, and let $\mathcal{F}$ be an equivariant simple perverse sheaf on $E$. Let the singular sup…

Integral-model intersection conjecture.

Let $X$ be a smooth variety over an algebraically closed field $k$ of characteristic $p\neq 2$, let $\mathcal{F}\in D(X)$, and let $(x,\xi)$ be a smooth point of $SS\mathcal{F}$. F…

Let $X$ be a smooth variety over an algebraically closed field $k$ of characteristic $p\neq 2$, and let $\mathcal{F}\in D(X)$. Write $SS\mathcal{F}$ for its singular support and le…

Suppose that $X$ is purely of dimension $d$ and that $D$ has simple normal crossings. Let $I'\subset I$ be a subset containing $I_{\mathrm{T},\mathcal{F}}$, and let … Assume that th…

Let $X$ be a smooth ambient space, let $f$ define the derived zero locus $\boldsymbol{Z}(f)$, and let $V^{\vee}$ be the ambient dual vector space. The source gives a closed immersi…

Let $X$ be a smooth ambient space and let $Z(f)\subset X$ be the zero locus of $f$. Model chains on $Z(f)$ using currents on $X$, and call a current smooth when it is represented b…

Microlocal characterization conjecture. Any irreducible $G_{\boldsymbol{d}}$-equivariant perverse sheaf on $E_{\boldsymbol{d}}$ whose singular support is contained in…

Laumon's conjecture on loose Hecke eigensheaves. A loose Hecke eigensheaf has a nilpotent singular support. This is presented as a special case of the preceding inclusion conjectur…

Let $G$ be a reductive group, let $X$ be a smooth proper curve, and let $\Dmod(\Bun_G)$ carry its Hecke action. Let $\Dmod_{\on{Nilp}}(\Bun_G)$ be the subcategory with nilpotent si…

Let $G$ be a reductive group, let $\mathfrak h$ be a Cartan subalgebra with Weyl group $W$, and let $v\in\mathfrak h^*/W$. Let $x\in\mathfrak g^*$ be a semisimple lift of $v$, and…

Let $k$ be a perfect field, and let $f\colon X\to Y$ be a morphism of smooth schemes over $k$. Assume that every irreducible component of $X$ has dimension $n$ and every irreducibl…

Let $G$ be a complex reductive group, let $X$ be a smooth complex projective curve, let $G^{\vee}$ be its Langlands dual group, and let $\mathcal Loc_{G^{\vee}}(X)$ be the Betti mo…

Global-nilpotent gluing conjecture. This functor is fully faithful.

Gluing Conjecture. This functor is fully faithful.