7 problems

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

Holonomicity conjecture. The relative characters of representations in $\mathcal{M}_{\Xi}(G)$ corresponding to $\Xi$-spherical subgroups should be regular holonomic.

Let $I_m$ be the $D_m$-ideal generated by the operators $P_1,\ldots,P_m$ defining the Muirhead ideal. An ideal is holonomic when its holonomic rank is finite. HNTT holonomicity con…

Let $D_n$ be the Weyl algebra in variables $x_1,\ldots,x_n$, let $J_{\rm diag}$ be the restriction ideal obtained from the ideal $J$ of differential operators annihilating the func…

Kontsevich's arithmetic-support conjecture. These Lagrangian subvarieties should be “fit together” to form a cycle for $M_{\mathbb{C}}$, called the arithmetic support, and this cyc…

Let $X$ be a complex manifold and let $f$ be a holonomic $f$-module on $X$. For each hypersurface $Z$ of $X$, consider the analytic slopes of $f$ along $Z$, namely the real numbers…

Let $A$ be a complex abelian variety, let $A^{\natural}$ be the space of line bundles with connection on $A$, and let $\operatorname{FM}_A$ denote the Fourier–Mukai transform. Let…