Generators for Certain Cyclic Extensions of Global Function Fields
โ Scribed by R.C. Valentini
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 200 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We show that, for all characteristic p global fields k and natural numbers n coprime to the order of the non-p-part of the Picard group Pic 0 (k) of k, there exists an abelian extension L/k whose local degree at every prime of k is equal to n. This answers in the affirmative in this context a questi
Suppose that L#K are abelian extensions of the rationals Q with Galois groups (Zรq s Z) n and (Zรq r Z) m , respectively, q any prime number. It is proved that LรK has a relative integral basis under certain simple conditions. In particular, [L : K] q s or q s +1 (according to q is odd or even) is e