Compatible ideals in Gorenstein rings

Abstract

Suppose $R$ is a $\mathbb{Q}$-Gorenstein $F$-finite and $F$-pure ring of prime characteristic $p>0$. We show that if $I\subseteq R$ is a compatible ideal (with all $p^{-e}$-linear maps) then there exists a module finite extension $R\to S$ such that the ideal $I$ is the sum of images of all $R$-linear maps $S\to R$.

Previous versions of the article proved the main theorem under the additional assumption that the $\mathbb{Q}$-Gorenstein index was relatively prime to the characteristic of $R$. Edits to the proof of the main theorem have been made

References in corpus (1)

• Finite torsors over strongly $F$-regular singularities