What Do You Know About The Artin Conductor?

10 Questions | Total Attempts: 103

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What Do You Know About The Artin Conductor? - Quiz

In the early 1930s, an Austrian mathematician of Armenian descent called Emil Artin introduced the Artin conductor as an expression appearing in the functional equation of an Artin L-function. In addition, the Artin conductor is used to define the conductor of an abelian variety or an elliptic curve and also appears in the conductor-discriminant formula for the discriminant of a global field.


Questions and Answers
  • 1. 
    Who invented the Artin conductor?
    • A. 

      Josh Artin

    • B. 

      Emil Artin

    • C. 

      Charles Artin

    • D. 

      Kyle Artin

  • 2. 
    What does L represent?
    • A. 

      Finite Galois Expression

    • B. 

      Infinite Galois Expression

    • C. 

      Length

    • D. 

      Logarithmic value 

  • 3. 
    What does K represent?
    • A. 

      Local field

    • B. 

      Surrounding field

    • C. 

      Keptic value

    • D. 

      Krystal value

  • 4. 
    Which character is the Artin conductor associated to? 
    • A. 

      Real number

    • B. 

      Galois value

    • C. 

      Galois group

    • D. 

      Logarithmic group

  • 5. 
    In which year was the theorem introduced? 
    • A. 

      1926

    • B. 

      1928

    • C. 

      1930

    • D. 

      1932

  • 6. 
    It appears as an expression in which equation? 
    • A. 

      Functional equation

    • B. 

      Simultaneous equation

    • C. 

      Multivariate value

    • D. 

      Polynomial equation

  • 7. 
    What does G represent?
    • A. 

      Galois group

    • B. 

      Galois value

    • C. 

      Galois equation

    • D. 

      Galois number

  • 8. 
    If L is unramified over K, then the Artin conductors of all χ are what?
    • A. 

      Zero

    • B. 

      One

    • C. 

      Two

    • D. 

      Three

  • 9. 
    The sum of the higher order terms is with which of these? 
    • A. 

      I < 0

    • B. 

      I > 0

    • C. 

      I = 1

    • D. 

      I = 2

  • 10. 
    How do we define the Artin representation Ag?
    • A. 

      The complex linear representation of G with this character

    • B. 

      The simple linear representation of G with this character

    • C. 

      The trigonometric representation of G with this character

    • D. 

      The exponential representation of G with this character

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