A prime-characteristic analogue of a theorem of Hartshorne-Polini

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Switala, Nicholas¹  Zhang, Wenliang¹ 

[1] Univ Illinois, Dept Math Stat & Comp Sci, 322 SEO M-C 249,851 S Morgan St, Chicago, IL 60607 USA

关键词: Mathis duality;    Local cohomology;    Frobenius modules;    F-modules;   

DOI  :  10.1016/j.jpaa.2020.106386

来源: Elsevier

【 摘 要 】

Let R be an F-finite Noetherian regular ring containing an algebraically closed field k of positive characteristic, and let M be an F-finite F-module over R in the sense of Lyubeznik (for example, any local cohomology module of R). We prove that the F-p-dimension of the space of F-module morphisms M -> E(R/m) (where m is any maximal ideal of R and E(R/m) is the F-injective hull of R/m) is equal to the k-dimension of the Frobenius stable part of Hom(R)(M, E(R/m)). This is a positivecharacteristic analogue of a recent result of Hartshorne and Polini for holonomic D-modules in characteristic zero. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free