11 problems

Asymptotic linear-bound conjecture. For every $p$ there exists a constant $A_p>0$ such that

Verlinde-fiber conjecture. Every STC fibers over $\operatorname{Ver}_{p^\infty}$.

Strict boundedness conjecture. The following assertions hold:

Etingof–Ostrik conjecture. The categories $\mathsf{Ver}_{p^n}$ should play the same role in positive characteristic as the category of supervector spaces plays in characteristic ze…

Let $p\geq5$, let ${\rm Ver}_p$ be the Verlinde category, and let $G$ be a linearly reductive height-$1$ subgroup scheme of $GL(Y)$ for an object $Y\in {\rm Ver}_p$. Let…

Ostrik's conjecture. The category $\mathcal{C}$ admits a fiber functor

Characteristic-$p$ universal property conjecture. Under certain conditions, symmetric monoidal functors

Cohomology algebra conjecture. The graded commutative $\mathbf{k}$-algebra

Let $\mathbf{k}$ be an algebraically closed field of characteristic $p>0$. A symmetric tensor category of moderate growth is a symmetric tensor category over $\mathbf{k}$ satisfyin…

Let $\mathcal{D}$ be a finite tensor category over a field $\mathbf{k}$ of characteristic $2$. Let $o(\mathcal{D})$ and $O(\mathcal{D})$ denote its lower and upper Frobenius orders…

Let $\mathcal{C}$ be an abelian symmetric tensor category of moderate growth over a field $\mathbf{k}$ of characteristic $p$. The Frobenius functor is the functor whose exactness d…