University of Illinois Urbana-Champaign

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

Kelm, Justin

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

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
Copyright and License Information
Copyright 2023 Justin Kelm

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