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arXiv · 1512.05374

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

Bhargav Bhatt·Linquan Ma·Karl Schwede
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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 $0\leq i 0$ or Du Bois in characteristic $0$, then the truncated dualizing complex $τ_{>-j}ω_R^\bullet$ 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.

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Bhargav Bhatt, Linquan Ma, Karl Schwede. 2017-07-18. The dualizing complex of $F$-injective and Du Bois singularities. https://doi.org/10.1007/s00209-017-1929-5

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