The category of F-modules has finite global dimension

JOURNAL OF ALGEBRA

卷:402

Article

Ma, Linquan

关键词: F-modules;   

DOI  :  10.1016/j.jalgebra.2013.12.008

来源: Elsevier

【 摘 要 】

Let R be a regular ring of characteristic p > 0. In [4], Hochster showed that the category of Lyubeznik's F-R-modules has enough injectives, so that every F-R-module has an injective resolution in this category. We show in this paper that under mild conditions on R, for example when R is essentially of finite type over an F-finite regular local ring, the category of F-modules has finite global dimension d + 1 where d = dim R. In [4], Hochster also showed that when M and N are F-R-finite FR-modules, Hom(FR) (M, N) is finite. We show that in general Ext(FR)(1), (M, N) is not necessarily finite. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free