6 problems

Let $(x \in X)$ be a singularity in characteristic zero. A singularity is of dense $F$-injective type if, for a model over a finitely generated $\mathbb{Z}$-subalgebra, the reducti…

Let $V$ be an $n$-dimensional projective simple normal crossing variety over an algebraically closed field of characteristic zero, and let $A$ be a finitely generated $\mathbb{Z}$-…

Let $Y$ be a smooth, irreducible variety over an algebraically closed field $k$ of characteristic zero, and let $\mathfrak{a}$ be a nonzero ideal on $Y$. Given any model $Y_A$ and…

Let $R$ be a finitely generated smooth commutative algebra over $\mathbb Z$, let $g\in\operatorname{Aut}(P_{n,R})$, and for each sufficiently large prime $p$ let $M_{g,p}$ be a bim…

Dense $F$-injective type conjecture. Being a $K$-algebra with dense $F$-injective type is equivalent to being a Du Bois singularity.

Let $X$ be a smooth, irreducible $n$-dimensional projective variety defined over an algebraically closed field $k$ of characteristic zero. If $X_A$ is a model of $X$ defined over a…