University of Illinois Urbana-Champaign

An ordinary rank-two case of local-global compatibility for automorphic representations of arbitrary weight over CM fields

Yang, Yuji

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https://hdl.handle.net/2142/115462

Description

Title
An ordinary rank-two case of local-global compatibility for automorphic representations of arbitrary weight over CM fields
Author(s)
Yang, Yuji
Issue Date
2022-04-15
Director of Research (if dissertation) or Advisor (if thesis)
Allen, Patrick Brodie
Doctoral Committee Chair(s)
Ahlgren, Scott
Committee Member(s)
  • Duursma, Iwan M
  • Thorner, Jesse Aaron
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • ordinary
  • local-global compatibility
Abstract
We prove a rank-two potential automorphy theorem for mod l representations satisfying an ordinary condition. Combined with an ordinary automorphy lifting theorem, we prove a rank-two, p-not-equal-to-l case of local-global compatibility for regular algebraic cuspidal automorphic representations of arbitrary weight over CM fields that is iota-ordinary.
Graduation Semester
2022-05
Type of Resource
Thesis
Copyright and License Information
Copyright 2022 Yuji Yang

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