The dualizing complex of $F$-injective and Du Bois singularities

Abstract

Let $(R,m,k)$ be an excellent local ring of equal characteristic. Let $j$ be a positive integer such that $H_m^i(R)$ has finite length for every $0\le i<j$. We prove that if $R$ is $F$-injective in characteristic $p>0$ or Du Bois in characteristic $0$, then the truncated dualizing complex ${\tau }_{>-j}{\omega }_R^{\bullet }$ is quasi-isomorphic to a complex of $k$-vector spaces. As a consequence, $F$-injective or Du Bois singularities with isolated non-Cohen-Macaulay locus are Buchsbaum. Moreover, when $R$ has $F$-rational or rational singularities on the punctured spectrum, we obtain stronger results.

13 pages, final version, to appear in Math.Z

References in corpus (2)

• $F$-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic $p>0$
• F-injectivity and Buchsbaum singularities

Cited by in corpus (1)

• Tight closure of parameter ideals in local rings $F$-rational on the punctured spectrum