What Do You Know About The Artin Conductor?

10 Questions | By AdeKoju | Last updated: Mar 19, 2022 | 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