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IntegralClosure :: conductor

conductor -- 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. 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.
conductor R

If the map is not icFractions(R), then pushForward is called to compute the conductor.

Caveat

Currently this function only works if F comes from a integral closure computation, or is homogeneous

See also

Ways to use conductor :