Abstract
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.
Original language | English |
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Pages (from-to) | 2127-2137 |
Number of pages | 11 |
Journal | Journal of Number Theory |
Volume | 128 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2008 |
Bibliographical note
Funding Information:* Fax: +82 2 3277 2289. E-mail address: [email protected]. 1 The author was supported by NSERC.
Keywords
- Divisor class group
- Ideal class group
- Quadratic function field
- Rank of divisor class group
- Reflection theorem