D-modules, V-filtrations, and B-functions in mixed characteristic

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Kelm, Justin

Contributors dc:contributor

• Dodd, Christopher
• Katz, Sheldon
• Heller, Jeremiah
• Bradlow, Stephen

• D-modules
• V-filtrations
• B-functions
• Mixed Characteristic
• Frobenius
• Lifts Of Frobenius

Statement dc:rights

• Copyright 2023 Justin Kelm

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121395

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121395