5 problems

Let $R$ be a normal $\mathbf{Q}$-Gorenstein ring. The lim-perfectoid log-canonicity conjecture. If $R$ is lim-perfectoid pure, then $R$ is log canonical. The paper proves the corre…

Suppose that $R\subseteq S$ is a finite $\mu_n$-quasi-torsor: there exists an open subset $U\subseteq\operatorname{Spec}R$ whose complement has codimension at least $2$, such that…

Let $R$ be a ring for which the notions of lim-perfectoid pure, perfectoid pure, lim-perfectoid injective, and perfectoid injective are defined. The lim-perfectoid comparison conje…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and let $(R,\mathfrak{m})\subseteq(S,\mathfrak{n})$ be a flat local homomorphism. The flat base-change conjecture. If $R$ is perfe…

Let $\mathrm{THR}(\mathbb{Z})$ denote the real topological Hochschild homology of the integers, regarded as a $\mathbb{Z}/2$-spectrum. Write $\mathrm{H}\\,\underline{\mathbb{Z}}$ f…