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conductor -- compute the conductor of a finite ring map

Synopsis

Description

Suppose that the ring map F : R --> S is finite: i.e. S is a finitely generated R-module. The conductor of F is defined to be {g ∈R  | g S ⊂f(R)}. One way to think about this is that the conductor is the set of universal denominators of S over R, or as the largest ideal of R which is also an ideal in S. On natural use is the conductor of the map from a ring to its integral closure.
i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);
i2 : S = integralClosure R

o2 = S

o2 : QuotientRing
i3 : F = R.icMap

o3 = map(S,R,{x, y, z})

o3 : RingMap S <--- R
i4 : conductor F

             3     2   3    4
o4 = ideal (z , x*z , x z, x )

o4 : Ideal of R

The command conductor calls the command pushForward. Currently, the command pushForward does not work if the source of the map F is inhomogeneous. If the source of the map F is not homogeneous conductor returns the message -- No conductor for F.

See also

Ways to use conductor :