3 problems

Let $S$ be a regular local ring, let $J$ be an $S$-ideal, and let $Y$ be a regular $S$-scheme obtained by a sequence of blow-ups at nonsingular centres such that $J\mathcal O_Y$ is…

Let $X$ be a normal $[?]$-Gorenstein closed subvariety of a smooth complex variety $A$. The adjoint-test ideal correspondence conjecture. After reduction to characteristic $p\gg0$,…

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…