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

Kelm, Justin

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

Description

Title

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

Author(s)

Kelm, Justin

Issue Date

2023-05-05

Director of Research (if dissertation) or Advisor (if thesis)

Dodd, Christopher

Doctoral Committee Chair(s)

Katz, Sheldon

Committee Member(s)

• Heller, Jeremiah
• Bradlow, Stephen

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• d-modules
• v-filtrations
• b-functions
• mixed characteristic
• frobenius
• lifts of frobenius

Abstract

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.

Graduation Semester

2023-08

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2023 Justin Kelm

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