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. An important case is the conductor of the map from a ring to its integral closure.
R = QQ[x,y,z]/ideal(x^7-z^7-y^2*z^5); |
icFractions R |
F = icMap R |
conductor F |
If an affine domain (a ring finitely generated over a field) is given as input, then the conductor of R in its integral closure is returned.
If the map is not
icFractions(R), then
pushForward is called to compute the conductor.