# What Do You Know About The Artin Conductor?

10 Questions | Total Attempts: 102  Settings  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.

• 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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