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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
- Handle URL
- https://hdl.handle.net/2142/121395
- Copyright and License Information
- Copyright 2023 Justin Kelm
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Graduate Dissertations and Theses at Illinois PRIMARY
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