Conductor of an integral closure
From Encyclopedia of Mathematics
The ideal of a commutative integral ring 
which is the annihilator of the 
-module 
, where 
is the integral closure of 
in its field of fractions. Sometimes the conductor is regarded as an ideal of 
. If 
is an 
-module of finite type (e.g., if 
is a geometric ring), a prime ideal 
of 
contains the conductor if and only if the localization 
is not an integrally-closed local ring. In geometrical terms this means that the conductor determines a closed subscheme of the affine scheme 
, consisting of the points that are not normal.
References
| [1] | N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French) |
| [2] | O. Zariski, P. Samuel, "Commutative algebra" , 1 , Springer (1975) |
How to Cite This Entry:
Conductor of an integral closure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conductor_of_an_integral_closure&oldid=12969
Conductor of an integral closure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conductor_of_an_integral_closure&oldid=12969
This article was adapted from an original article by I.V. Dolgachev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article