146 problems

Let $G$ be a complex reductive group, let $X$ be a smooth complex projective curve, and let $G^{\vee}$ be its Langlands dual group. Let $\mathfrak{\det}$ denote the determinant line…

Let $X$ be a smooth projective curve over an algebraically closed field of characteristic zero, let $G$ be a reductive group, and let $\check G$ be its Langlands dual group. Under…

Let $G=\operatorname{GL}_r$. Let $\mathcal{B}\subset(\mathrm{B}_{\operatorname{GL}_r}^{\mathrm{red}})^{\mathrm{cl}}$ be an open subset, and set … Let…

Let $k$ be a field, let $X$ be a smooth projective curve over $k$, and let $G$ be a reductive group over $k(X)$ with Langlands dual group $\LG$. Let $S\subset X$ be a finite set. F…

Let $G$ be a reductive group, let $P\subset G$ be a standard parabolic with Levi subgroup $M$, and let $\bP\subset \bG$ be the corresponding parabolic in the Langlands dual group w…

Let $G$ be a semisimple simply-laced complex group, let $\theta$ be a diagram automorphism of $G$, and let $C$ be a Calabi–Yau Riemann surface. For any…

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

Coincidence conjecture. The isomorphisms supplied by Proposition 'IC calculation' and Theorem 'FFKM thm' (1) coincide. This is a compatibility assertion internal to the proof of th…

The geometric Langlands correspondence. There exists a canonical equivalence of categories

The geometric Langlands correspondence. There exists a canonical equivalence of categories

Full Hecke-property conjecture. Then ${\mathcal S}_E$ satisfies the full Hecke property.

Let $G$ be the group in the paper, let $P$ be a standard proper parabolic with Levi subgroup $M$, and let $W$ be an irreducible local system on $X$ of rank $r=\dim V^\gamma$. For…

Let $G$ be the group and let $\gamma$ be the coweight used to define the stacks $\mathcal Y_d$. For a $\check{G}$-local system $E$ on $X$, let $\mathcal W^d_{E,\psi}$ be the Whitta…

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…

Fix a cocompact lattice $J\subset Z(\mathbbA)/Z(F)$ and an admissible $n$-tuple $\overline{\omega}$. Let … be the cuspidal intersection cohomology representation, and let…

The averaging-functor vanishing conjecture. Assume that $E$ is irreducible and has rank greater than $n$. If

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…

Gaitsgory–Lurie quantum fundamental local equivalence conjecture. The functor $\operatorname{FLE}$ is an equivalence.

Let $G$ be a reductive group, let $\check{G}$ be its Langlands dual group, and let $\operatorname{Shv}_{c,\operatorname{Nilp}}(\operatorname{Bun}_G)$ denote the category of $c$-twi…

Let $G$ be a simple reductive group, let $\check{G}$ be its Langlands dual group, let $\check{h}$ be the dual Coxeter number of $G$, and let $r$ be the maximal multiplicity of arro…

Let $G$ be a reductive group, let $\chi\in\pi_1(G)$ and let $w\in Z_G^{\vee}$, where $Z_G$ is the center of $G$. Let $\mathrm{Higgs}_G(\chi)$ denote the connected component of the…

Let $C$ be a smooth projective curve, let $G$ be a reductive group with Langlands dual group $G^{\vee}$, and let $w$ denote the relevant stratum or weight. Write…

Let $\mathbf{L_H(d)}$ be the Fourier transform associated with the Lagrangian correspondence $\mathbb L_H(d)$, and let $\mathbf{q\text{-}L_H(d)}$ be its quantization to a functor ……

Let $\mathbb L_H(d)$ be the Lagrangian correspondence constructed between the relevant Hitchin moduli space and the Hilbert scheme of points on $T^*C$, and let the Dolbeault geomet…

Let $G$ be a reductive group with involution $\theta$, let $X_\theta=G^{\operatorname{inv}\circ\theta}=\{g\in G\mid\theta(g)=g^{-1}\}$ with its $\theta$-twisted conjugation action,…