We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field Fq. Let L1 be a quadratic geometric extension of K and let L2 be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L1 and L2 have the same m-rank.
Bibliographical noteFunding Information:
* Fax: +82 2 3277 2289. E-mail address: email@example.com. 1 The author was supported by NSERC.
- Divisor class group
- Ideal class group
- Quadratic function field
- Rank of divisor class group
- Reflection theorem