A dichotomy for the injective dimension of F-finite F-modules and holonomic D-modules. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Switala, Nicholas; Zhang, Wenliang
• Is Part Of: Communications in algebra. Volume 47:Issue 6(2019)
• Page Start: 2525
• Page End: 2539
• Publication Date: 2019-06-03
• Subjects: D-modules -- F-modules -- local cohomology; Primary 13N10 -- 13A35 -- secondary 13D45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1501574
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let M be either a holonomic D -module over a formal power series ring with coefficients in a field of characteristic zero, or an F -finite F -module over a noetherian regular ring of characteristic p > 0. We prove that injdim R M enjoys a dichotomy property: it has only two possible values, dim Supp R M − 1 or dim Supp R M .