What Do You Know About The Artin Conductor?

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What Do You Know About The Artin Conductor?

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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