Ray Class Group
The ray modulo m is
A modulus m can be split into two parts, mf and m∞, the product over the finite and infinite places, respectively. Let Im to be one of the following:
- if K is a number field, the subgroup of the group of fractional ideals generated by ideals coprime to mf;
- if K is a function field of an algebraic curve over k, the group of divisors, rational over k, with support away from m.
In both case, there is a group homomorphism i : Km,1 → Im obtained by sending a to the principal ideal (resp. divisor) (a).
The ray class group modulo m is the quotient Cm = Im / i(Km,1). A coset of i(Km,1) is called a ray class modulo m.
Erich Hecke's original definition of Hecke characters may be interpreted in terms of characters of the ray class group with respect to some modulus m.
Read more about this topic: Modulus (algebraic Number Theory)
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