How Much Do You Know About Arthur's Conjectures?

10 Questions | Total Attempts: 104

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How Much Do You Know About Arthur

Arthur's conjectures is a noted mathematical theorem paper written in 1989 by James Arthur. Arthur is the former president of the American Mathematical Society and a Professor at the University of Toronto. His conjectures deal with Unipotent Automorphic Representations on local and global scales. Test your knowledge with this quiz!


Questions and Answers
  • 1. 
    What is the overall purpose of Arthur's Conjectures?
    • A. 

      Make sense of semisimple and unipotent representations of automorphic forms.

    • B. 

      Describe how conjectures relate to the spectral side of the trace formula.

    • C. 

      Show the functorial lifting of a reductive group.

    • D. 

      Prove Z(H) is the center of group H.

  • 2. 
    What does Arthur mean by unipotent?
    • A. 

      Dealing only with local conjectures.

    • B. 

      Dealing only with global conjectures.

    • C. 

      A subgroup where all elements remain unchanged in value when operated on by themselves.

    • D. 

      A subgroup having only one element that is unchanged in value when operated on by itself.

  • 3. 
    A simplistic form of Arthur's conjectures split automorphic representations into ________, and a refined form used ________ representations.
    • A. 

      Individuals, Group

    • B. 

      Packets, Individual

    • C. 

      Groups, Parabolic

    • D. 

      Parabolas, Packet

  • 4. 
    Which formula are Arthur's Conjectures based on? 
    • A. 

      Derivative Formula

    • B. 

      Trace Formula

    • C. 

      Inverse Function Formula

    • D. 

      Law of Sines Formula

  • 5. 
    Arthur's mentor, Robert Langlands, created a notion of Functoriality that Arthur worked off of. Simply put, what was the difference in the mens' work?
    • A. 

      Langlands worked with functorial lifting of unitary characters. Arthur worked with lifting of a reductive group

    • B. 

      Langlands proved functoriality for non-Archimedean fields. Arthur worked on Archimedean fields

    • C. 

      Langlands worked with functorial lifting of a reductive group. Arthur worked with lifting of unitary characters

    • D. 

      Langlands and Arthur's work have no differences because they always worked together

  • 6. 
    What is a reductive group?
    • A. 

      Parabolic algebraic group of points centering on a line

    • B. 

      Linear algebraic group over a field

    • C. 

      Clustered algebraic group over a field

    • D. 

      Geometric points forming a line over a field

  • 7. 
    A large amount of Arthur's work deals with Endoscopy. Who is responsible for the theory of endoscopy?
    • A. 

      Langlands and Shelstad

    • B. 

      Langlands and Bell

    • C. 

      Arthur and Shelstad

    • D. 

      Friberg and Grioux

  • 8. 
    Why did Arthur need to consider endoscopy?
    • A. 

      Endoscopy hasn't been proven with tempered representations and he had a hypothesis on how to do so

    • B. 

      In order to understand linear groups better he needed to use elements of endoscopy

    • C. 

      He wanted to apply his theory to non-tempered representations, where he needed to consider endoscopic groups.

    • D. 

      He worked with endoscopic groups to create reductive groups

  • 9. 
    By changing the parameters of Langlands research, Arthur's Conjectures encountered which problems (according to a 2004 paper by Laurent Clozel)?
    • A. 

      Algebraic and linear

    • B. 

      Combinatorial, representation-theoretic and arguably geometric

    • C. 

      Automorphic-representative and geometric

    • D. 

      Functoriality

  • 10. 
    A 2009 study by O. Paniagua- Taboada also found what issue with an elliptic Arthur parameter?
    • A. 

      Cannot calculate the twisted characters

    • B. 

      The ellipse cannot be complete

    • C. 

      The parameters cannot be cuspidal

    • D. 

      The parameters cannot be linear

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