Let L#F be cyclotomic function fields of Carlitz. We show that if LΓF is Carlitz Kummer, the integer ring O L is free over the associated order as in the classical cyclotomic Kummer extension. However, contrary to the characteristic zero case, O L is not free unless LΓF is Carlitz Kummer.
β¦ LIBER β¦
Carlitz Modules and Galois Module Structure
β Scribed by Akira Aiba
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 609 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
β¦ Synopsis
Let k be a one variable rational function field over a finite field. We construct an example of a wildly ramified abelian extension over k, whose integer ring is not free over its associated order.
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