153 problems

Let $F$ be the tuple of functions and let $B_F^{\mathbf{m}_1,\dots,\mathbf{m}_p}$ denote the associated ideal in the variables $s_1,\dots,s_r$, where…

Let $X$ be a complex manifold and let $\mathcal{M}$ be a semisimple holonomic $\mathcal{D}$-module on $X$. The results described for regular holonomic $\mathcal{D}$-modules should…

Let $X$ be a complex manifold, let $\mathcal{D}_X$ be its sheaf of differential operators, and let $\mathcal{M}\in D^b_h(\mathcal{D}_X)$ be a bounded complex with holonomic cohomol…

Let $(G,K)$ be a symmetric pair, and let the corresponding invariant eigendistributions be solutions of a holonomic $\mathcal D$-module. Sekiguchi's conjecture. In the more general…

Let $X$ be the underlying smooth variety, and let $\mathcal{M}$ be a holonomic $\widehat{\mathcal{A}\mathcal{V}}$-module. Here holonomicity is the finiteness condition used in the…

Let $\mathcal{X}$ be a smooth QCA stack, and let $\operatorname{L}(\Omega_{\mathcal{X}})_{1/2}$ be the half-twisted limit category associated with its cotangent stack. For a cohere…

Bitoun–Schedler's conjecture. The length of ${\mathcal D}_Xf^{-1}$ should be

Takayama's conjecture. The holonomic dual of an $A$-hypergeometric system is itself a GKZ system.

Let $\rho:\widetilde X\to X$ be a symplectic resolution, with $X$ affine, and let $\operatorname{\mathsf{HP}}_i^{DR}(X)$ denote the Poisson-de Rham homology of $X$. The affine symp…

Let $d=(d_K)_{K\in{[m]\choose n}}$ be the tuple of maximal minors of a generic $m\times n$ matrix. For each $\alpha\in\mathbb{Z}$, let $F_{\alpha}$ be the $\mathcal{D}$-module asso…

Let $M$ be a complex manifold and let $\nabla$ be a flat meromorphic connection on $M$. A formal decomposition of $\nabla$ is called good when its formal exponential factors satisf…

Let $X$ be a complex manifold, let $\mathscr{M}$ be a coherent bounded complex of $\mathscr{D}_X$-modules, and let $\Lambda$ contain $\operatorname{char}(\mathscr{M})$. Choose a go…

Minimal-resolution conjecture. In the homogenized Weyl algebra, a minimal resolution exists and can be constructed by the algorithm in LaScala, since the algebra is graded; however…

Projective-cover and homological-dimension conjecture. The category $Qui_\lambda({\cal A})$ should contain the projective covers and have homological dimension at most $N$.

Mellin–solution commutation conjecture. There exists a canonical isomorphism

Constructibility conjecture. The complex $\mathcal{S}ol^{<0}(\mathcal{M})$ has $\mathbb{C}$-constructible cohomology sheaves.

Brylinski's conjecture. The associated filtration on $\operatorname{dR}(\mathcal{M})$ induces the desired Hodge structure on $IH_\bullet(X)$.

Let $A$ be an integer matrix, let $\mathcal{M}_A(\beta)$ be the projectivized $A$-hypergeometric system with parameter $\beta$, and let $Y$ be a coordinate variety. For a filtratio…

Let $A$ be fixed, let $L$ be a filtration, let $\tau$ be the corresponding face or stratum, and let $\mu^{L,\tau}_{A,0}(\beta)$ denote the multiplicity of the associated component…

Let $\pi:{\mathfrak X}\to S[[h]]$ and the quantization sheaf $\operatorname{\cal O}_h$ satisfy the assumptions of Theorem. Consider the global sections functor … from sheaves of fi…

Kashiwara–Schapira's regularity conjecture. The module $\mathcal{M}$ is regular holonomic if and only if…

Hypergeometric pullback conjecture. For every constituent $\mathcal{C}$ of $Q$, there exist a torus $T_{\mathcal{C}}$, a morphism of tori

Let $A$ be an integer matrix, let $S_A$ be its semigroup ring, and let $\mathfrak m$ be its homogeneous maximal ideal. For each $i<\dim(S_A)$, let $H^i_{\mathfrak m}(S_A)$ denote t…

Let ${\mathsf{H}}_c$ be the rational Cherednik algebra of type ${\mathfrak{gl}}_n$ with parameter $c\in\mathbb{C}$, and let ${\mathsf{e}}$ be the symmetrizer idempotent for $S_n$.…

Let $\hat\fg_{crit}\text{--}\on{mod}^{G(\wh{\CO}_x)}_{\nil}$ be the category of $G(\CO_x)$-integrable critical-level $\hat\fg$-modules that are set-theoretically supported on…