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Conductor


In number theory, a conductor is an arithmetic invariant that records the primes at which an object is ramified or has bad reduction, together with local exponents measuring the severity. Many conductors have the form

 N=product_(p)p^(f_p),

where the f_p are conductor exponents. Important examples include the Artin conductor and the elliptic curve conductor.


See also

Artin Conductor, Conductor Exponent, Elliptic Curve Conductor, Ramification

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References

Serre, J.-P. Local Fields. New York: Springer-Verlag, 1979.

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Conductor

Cite this as:

Weisstein, Eric W. "Conductor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Conductor.html

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