The conductor of an abelian variety $A$ over $\Q$ is a positive integer $N$ whose prime factors are the primes $p$ where $A$ has bad reduction. The power to which $p$ divides $N$ depends on the type of bad reduction, and is related to the ramification in the $p$-torsion field of the abelian variety.
The conductor of an abelian variety over a number field is defined similarly; it is an ideal that is a product of non-trivial powers of the prime ideals where $A$ has bad reduction. The conductor of a curve $C$ over a number field is defined to be the conductor of the Jacobian of $C$.
The conductor is an invariant of the isogeny class of an abelian variety.
- Review status: reviewed
- Last edited by Andrew Sutherland on 2017-06-30 22:35:08
- lmfdb/genus2_curves/main.py (line 931)
- lmfdb/genus2_curves/templates/g2c_browse.html (line 12)
- lmfdb/genus2_curves/templates/g2c_curve.html (line 55)
- lmfdb/genus2_curves/web_g2c.py (line 611)