10 problems

Finite-order translation conjecture. The characteristic variety is a union of translated subtori, with each translation given by a point of finite order.

Quasi-adjunction characteristic-variety conjecture. The Zariski closure of $\exp(\mathcal F)\subset\operatorname{Char}H_1(U,\mathbb Z)$ is a component of the characteristic variety…

Translated-subgroup support conjecture. The support of $\pi_n(\partial B_{\epsilon}-D)$ is a union of translated subgroups of $\operatorname{Char}\pi_1(\partial B_{\epsilon}-D)$ by…

Torsion-translation conjecture. The characteristic variety is a union of translated subtori of

Let $[m]=\{1,\ldots,m\}$, and let $I_m$ be the Muirhead ideal in the Weyl algebra $D_m$. For a partition $[m]=J_0\sqcup J_1\sqcup\cdots\sqcup J_k$, where $J_0$ may be empty, the ot…

Let $(M,\mathcal{I})$ be an involutive exterior differential system. Let $\dot{\Xi}$ and $\Xi_E$ be the characteristic varieties defined in the surrounding discussion, viewed as su…

Bryant–Griffiths–Yang conjecture. The characteristic variety $\Sigma({\bf c})$ is not smooth in $\mathbb R^n\setminus\\{0\\}$ for every $n\ge 5$.

Let $R$ be the base ring, let $\mathscr{X}$ be a smooth formal scheme of finite type over $R$, and let $\mathscr{M}$ be a coherent $\mathscr{D}^{(m)}_{\mathbb{Q},\mathscr{X}}$-modu…

Let $R$ be the base ring, let $\mathscr{X}$ be a smooth formal scheme of finite type over $R$, and let $\mathscr{M}$ be a $\mathscr{D}^{\dagger}$-module. Let…

Let $\operatorname{Bun}_H$ be the stack of $H$-bundles, let ${\cal K}_H$ be the perverse sheaf constructed in the paper, and let ${\cal C}^0\subset T^*\operatorname{Bun}_H$ be the…