76 problems

Let $X$ be a complex variety, let $\mathcal{M}$ be a holonomic $\mathcal{D}$-module on $X$, and let $S(\mathcal{M})$ be the union, over germs of hypersurfaces $Z$ of $X$, of the se…

Let $X$ be a complex manifold of dimension $d$, and let ${\cal M}^\bullet$ be a complex of ${\cal D}_X$-modules with bounded good cohomology. Choose a filtration compatible with th…

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…

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…

Annihilator-generator conjecture. For any central arrangement $Q$,

Regularity conjecture. The module $\mathcal{M}$ is regular holonomic if and only if $Sol^t(\mathcal{M})$ is regular. The text notes that the only-if direction follows from the prec…

Real-constructibility conjecture. The ind-sheaf $Sol^t(\mathcal{M})$ belongs to $D^b_{\mathbb{R}\text{-c}}(\mathrm{I}[\mathbb{C}_X])$. This is presented as a consequence of the pap…

Let $X$ be a complex manifold of dimension $d$, let ${\cal M}^\bullet$ be an object of $\operatorname{D}^b_{good}({\cal D}^{op}_X)$, and let $\Lambda$ be a conic subvariety of…

Consequences conjecture. For generic choices of $u\in\mathbb{C}^{n+1}$:

Integral representation conjecture. For generic choices of $u\in\mathbb{C}^{n+1}$, the morphism $\psi$ is an isomorphism of $D_Z$-modules.

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 $X$ be a smooth scheme. Consider the non-linear $\mathcal{D}$-Fredholm index, its symbol complex, and the cycle defined by the associated graded symbol morphism in the total sp…

Let $X$ be the underlying space, let $\mathcal{M}$ be a regular holonomic $\mathscr{D}_X$-module, and let $\mathcal{N}_0$ be the associated module. For a monoid ideal…

Let $G$ be a connected algebraic group, let $n$ be a rank, and let $q\colon G\twoheadrightarrow G/[G,G]$ be the quotient map. Write $\sim$ for the relation of $D$-module isomorphis…

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…

Derived D-module equivalence. There exists a symmetric monoidal equivalence

Let $q$ be a complex number that is not a root of unity, and let $G=\operatorname{GL}_2$ or $G=\operatorname{SL}_2$. A $\mathcal{D}_q(G)$-module is called strongly equivariant when…

Let $C=\mathbb{P}^1$ and let $\operatorname{Bun}_{\operatorname{GL}_r}(0)$ be the degree-zero component of the moduli stack of rank-$r$ vector bundles. Let…

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…

Let $M$ be a complex manifold, let $D\subset M$ be a free divisor, and suppose that $D$ satisfies the logarithmic comparison theorem. Let $M$ be regarded as the ambient constructib…

Invariant D-module abelianization conjecture. The pull-back induces an isomorphism

Let $\check G$ be the Langlands dual group, let $V\in\operatorname{Rep}(\check G)$, and let $\nabla_{\check G}^{\mathrm{H}}(V)$ be the rescalable integrable mixed twistor module as…

Let $L$ be a simple $\mathfrak{g}$-module and let $V$ be a finite-dimensional $\mathfrak{g}$-module. A strange subquotient of $V\otimes_{\mathbb{C}}L$ is a non-simple subquotient h…