11 problems

Mascia–Rinaldo–Romeo conjecture. The following conditions are equivalent:

Let $n$ be a positive integer, let $\boldsymbol{\rm Mat}^{\mathrm{sym}}_{n\times n}$ be the space of symmetric $n\times n$ matrices, and for each symmetric matrix…

Let $k$ be an algebraically closed field, let $\mathcal{C}$ be a tensor category of moderate growth, and let $A\in\mathsf{Alg}\mathcal{C}$ be an algebra object. A prime ideal…

Let $R$ be a Noetherian ring, complete with respect to a positive filtration topology, and let $(\sigma,\delta)$ be a continuous skew derivation compatible with the filtration. Def…

Let $W$ be the Witt algebra, let $\operatorname{U}(W)$ be its universal enveloping algebra, and let $\pi_\gamma$ be the family of representations defined in the paper, with kernels…

Let $W$ be the Witt algebra and let $\operatorname{U}(W)$ be its universal enveloping algebra. The Witt prime-to-primitive containment conjecture. Every proper prime ideal of…

The standardness conjecture. Let $G$ be a solvable, uniform pro-$p$ group, and let $P$ be a prime ideal in $\mathcal{O}G$. Then $P$ is virtually standard, and moreover if $p\in P$…

Let $G$ be a split, simply connected, semisimple algebraic group over a field $K$ of characteristic zero, let $P_I$ be the standard parabolic subgroup associated with a set of simp…

Let $K$) be a number field of bounded degree $n$ over $\mathbb{Q}$, with discriminant $D_K$ and class number $h_K$. An ideal class is said to contain a prime ideal if some prime id…

Let $S=\mathbb{C}[x_1,x_2,x_3,x_4]$. The prime-ideal conjecture for pairs of power sums. The following assertions hold: (1) if $a$ is prime, $a\ge5$, and $b=a+m+6d$ with…

Growth-constant bound conjecture. There exists a function $F:(0,\infty)\rightarrow(0,\infty)$ such that $A$ has at most $F({\rm GC}(A))$ prime ideals $P$ satisfying…