9 problems

Let $U_\zeta(\mathfrak g)$ be the quantum group, let ${}^fU_\zeta(\mathfrak g)$ be the indicated subalgebra, and let $Z_{\rm Har}(U_\zeta(\mathfrak g))$ be its Harish–Chandra cente…

Let $R$ be a commutative ring, let $I$ be an ideal of $R$, let $V$ be an $R/I$-module, and let $P.(V)$ be a projective resolution of $V$ over $R$. Write $N$ for normalization,…

Let $A$ be an associative algebra, let $\overline{\varphi}$ be the map in the preceding kernel-presentation conjecture, and define $\theta_2(A)=[A,A]/[A,[A,A]]$. Replacing $A$ by a…

Let $V$ be a ${\mathscr{A}}_{n,\lambda,\nu}$-module, and let $F_i$ be the functor defined in the paper. Write $H^r({\mathscr{C}}^\bullet(V))$ for the $r$-th cohomology of the compl…

Let $I,J\subseteq\Delta$, let $\sigma$ be a locally admissible smooth representation of $L_I$ over $A$, let ${}^Iw^J\in{}^IW^J$, and let $n\in\mathbb{N}$. Let $d_{{}^Iw^J}$ and…

Derived-functor conjecture. The inverse limit

Unstable filtration conjecture. The derived functors $L_*\Gamma(A,n)$ admit a filtration whose associated graded pieces are described by the restricted admissible-word summands ind…

Let $\mathfrak{k}\simeq\mathfrak{sl}(2)$, and let $\lambda_1,\lambda_2$ be the parameters occurring in the paper's setup. For $n\geq 0$, consider the categories…

Higher derived-functor vanishing conjecture. The derived functors of order greater than one annihilate the global sections: