2 problems

Negative-invariant conjecture. If $\operatorname{char}(k)=0$ and $b(R)<0$, then $R$ is of strongly F-regular type. If, moreover, $R$ is $\mathbb Q$-Gorenstein, meaning that…

Let $R$ be an algebra over the finite field $\mathbb{F}_p$. A finite cover of $R$ is called split when the inclusion of $R$ into the cover admits an $R$-linear retraction; $R$ is a…