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Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 1143–1155 | Cite as

The dualizing complex of F-injective and Du Bois singularities

  • Bhargav Bhatt
  • Linquan Ma
  • Karl Schwede
Article

Abstract

Let \((R,\mathfrak {m}, k)\) be an excellent local ring of equal characteristic. Let j be a positive integer such that \(H_\mathfrak {m}^i(R)\) 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 Open image in new window 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).

Keywords

F-injective Du Bois Dualizing complex Local cohomology 

Mathematics Subject Classification

14F18 13A35 14B05 

Notes

Acknowledgements

We would like to thank Shunsuke Takagi for several useful discussions and for bringing these questions to our attention. We would also like to thank Sándor Kovács, Zsolt Patakfalvi and Sean Sather-Wagstaff for useful discussions. Finally we thank Lance Miller, Kazuma Shimomoto and the referees for comments on previous drafts of this paper.

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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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