The dualizing complex of F-injective and Du Bois singularities

Let (R,m,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(R,\mathfrak {m}, k)$$\end{document} be an excellent local ring of equal characteristic. Let j be a positive integer such that Hmi(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\mathfrak {m}^i(R)$$\end{document} has finite length for every 0≤i<j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le i <j$$\end{document}. We prove that if R is F-injective in characteristic p>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>0$$\end{document} or Du Bois in characteristic 0, then the truncated dualizing complex [inline-graphic not available: see fulltext] 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 generalizing Ishida (The dualizing complexes of normal isolated Du Bois singularities. Algebraic and topological theories, 387–390, 1984) and Ma (Math Ann 362:25–42, 2015).