5 problems

Let $(R,\frak{m})$ be an excellent Noetherian local ring of characteristic $p>0$ such that its completion $\widehat{R}$ is reduced and satisfies $(S_2)$. For a parameter ideal…

Let $R$ be an excellent Noetherian domain of characteristic $p>0$. Denote by $\tau_{\rm fg}(R)$ the finitistic test ideal and by $\tau_{\rm b}(R)$ the big test ideal of $R$. Test i…

Let $(R,\operatorname{\mathfrak{m}})$ be a $d$-dimensional complete local domain of mixed characteristic $p$. Assume that $p,x_2,\dots,x_d$ is a system of parameters. Set … and, fo…

Strong-versus-weak F-regularity conjecture. $R$ is strongly $F$-regular if and only if

Let $(R,\mathfrak{m})$ be a regular local ring essentially of finite type over a perfect field of prime characteristic $p$, and let $I \subseteq R$ be a nonzero unmixed ideal. Let…