Strong F-regularity and generating morphisms of local cohomology modules

JOURNAL OF ALGEBRA

卷:525

Article

Katzman, Mordechai¹  Miranda-Neto, Cleto B.² 

[1] Univ Sheffield, Dept Pure Math, Hicks Bldg, Sheffield S3 7RH, S Yorkshire, England

[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, PB, Brazil

关键词: Tight closure;    Strongly F-regular;    F-rational;    F-pure;    Local cohomology;    Determinantal ring;   

DOI  :  10.1016/j.jalgebra.2018.12.030

来源: Elsevier

【 摘 要 】

We establish a criterion for the strong F-regularity of a (non-Gorenstein) Cohen-Macaulay reduced complete local ring of dimension at least 2 and prime characteristic p. We also describe an explicit generating morphism (in the sense of Lyubeznik) for the top local cohomology module with support in certain ideals arising from an n x (n - 1) matrix X of indeterminates. For a perfect field k of characteristic p >= 5, these results led us to derive a simple, new proof of the well-known fact that the generic determinantal ring over k given by the maximal minors of X is strongly F-regular. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free