Galois module structure of the integers in weakly ramified extensions
β Scribed by G. Griffith Elder; Manohar L. Madan
- Publisher
- Springer
- Year
- 1995
- Tongue
- English
- Weight
- 236 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
For a finite unramified Galois -extension of function fields over an algebraically closed field of characteristic different from , we find the Galois module structure of the elements of the Jacobian whose orders are powers of .
Let p be an odd prime number and k a finite extension of Q p . Let K/k be a totally ramified elementary abelian Kummer extension of degree p 2 with Galois group G. We determine the isomorphism class of the ring of integers in K as an oG-module under some assumptions. The obtained results imply there
Let k be a number field with ring of integers O k , and let be the dihedral group of order 8. For each tame Galois extension N/k with group isomorphic to , the ring of integers O N of N determines a class in the locally free class group Cl(O k [ ]). We show that the set of classes in Cl(O k [ ]) rea