Conductor Ideal

The conductor ideal of an inclusion of commutative rings is

It is the largest ideal of contained in and equals the annihilator of the -module . For the algebraic normalization of a reduced algebraic variety, its sheaf version measures where the algebraic normalization differs from the original algebraic variety (Stacks Project n.d.). For example, the inclusion has conductor , generated by as an ideal of the smaller ring. The conductor boundary on algebraic normalization components is part of the definition of a semi-log canonical pair (Fujino 2014, p. 202).