2026-09-22T07:55:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/121395 2023-12-13 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Dodd, Christopher Katz, Sheldon Heller, Jeremiah Bradlow, Stephen 2023-08 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms The student, Justin Kelm, accepted the attached license on 2023-05-04 at 15:30. The student, Justin Kelm, submitted this Dissertation for approval on 2023-05-04 at 15:37. This Dissertation was approved for publication on 2023-05-05 at 11:08. DSpace SAF Submission Ingestion Package generated from Vireo submission #19336 on 2023-12-04 at 16:59:37 D-modules, V-filtrations, and B-functions in mixed characteristic Kelm, Justin 2023-05-05 D-modules V-filtrations B-functions Mixed Characteristic Frobenius Lifts Of Frobenius Within the existing literature, the theory of D-modules tends to bifurcate depending on whether the underlying based field is assumed to be of finite characteristic. The techniques used in either case may diverge greatly, but many results can be unified. In this paper we elaborate on this unification in the context of b-functions and V-filtrations by means of mixed characteristic arguments, emphasizing the role of Berthelot’s rings of differential operators as a translational tool. In particular, we present a proof in mixed characteristic of Kashiwara’s equivalence, give a definition in mixed characteristic of V-filtrations, and delineate the simultaneous eigenspace structure of said V-filtrations. Text eng https://hdl.handle.net/2142/121395 Copyright 2023 Justin Kelm Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics