9 problems

Let $(R,\mathfrak{m},K)$ be a local ring, let $I$ be an ideal of $R$, let $c$ be the cohomological dimension of $I$, and let $J=\operatorname{Ann}_R H^c_I(R)$. Lynch's conjecture.…

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

Let $V$ be an indecomposable ${\mathfrak b}$-trivial extension of $L$ tensor density modules ${\mathcal F}_{\lambda_1},\ldots,{mathcal F}_{\lambda_L}$, with…

Fix $\delta=3$, and let ${\mathcal A}_3$ be the annihilator of the universal difference-$3$ extension, the direct sum over all $\lambda$ of the extensions of ${\mathcal F}_\lambda$…

Let $V$ be the ${\mathop{\rm Vec}\nolimits(\mathbb R)}$-submodule described above, an extension of $\mathbb C$ by ${\mathcal F}_1$, and let $Q$, $Y$, and $Z$ be the operators actin…

Let $R$ be a local ring and let $\mathfrak a$ be a proper ideal of $R$. Write … Let $\Gamma_{\mathfrak a}(R)$ denote the $\mathfrak a$-torsion submodule of $R$, and let…

Let $V$ be a finite-dimensional vector space over a field $F$, let $E(V)$ be its exterior algebra, and let … be a neat element, where each $\xi_k$ is decomposable and has even degr…

Solomon's conjecture. The element $\operatorname{sol}_F$ annihilates

Let $\mathfrak{g}$ be in the setup of the preceding construction, let $\mu\in\mathfrak{h}^*$ be such that the Verma module $M(\mu)$ is simple, and let…