Download PDF - Relative Galois module structure of integers of local abelian fieldsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Relative Galois module structure of integers of local abelian fields

Authors 1

Affiliations

  1. Institut für Mathematik, Karl-Franzens-Universität, Heinrichstrasse 36, A-8010 Graz, Austria

Bibliography

  1. F. Bertrandias et M.-J. Ferton, Sur l'anneau des entiers d'une extension cyclique de degré premier d'un corps local, C. R. Acad. Sci. Paris Sér. A 274 (1972), 1330-1333.
  2. W. Bley, A Leopoldt-type result for rings of integers of cyclotomic extensions, Canad. Math. Bull. 38 (1995), 141-148.
  3. J. Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157-166.
  4. N. P. Byott, Galois structure of ideals in wildly ramified abelian p-extensions of a p-adic field, and some applications, J. Théor. Nombres Bordeaux 9 (1997), 201-219.
  5. N. P. Byott and G. Lettl, Relative Galois module structure of integers of abelian fields, ibid. 8 (1996), 125-141.
  6. S.-P. Chan and C.-H. Lim, Relative Galois module structure of rings of integers of cyclotomic fields, J. Reine Angew. Math. 434 (1993), 205-220.
  7. L. Childs, Taming wild extensions with Hopf algebras, Trans. Amer. Math. Soc. 304 (1987), 111-140.
  8. L. Childs and D. J. Moss, Hopf algebras and local Galois module theory, in: Advances in Hopf Algebras, J. Bergen and S. Montgomery (eds.), Lecture Notes in Pure and Appl. Math. 158, Dekker, Basel, 1994, 1-24.
  9. C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. I, Pure Appl. Math., Wiley, 1981.
  10. A. Fröhlich, Invariants for modules over commutative separable orders, Quart. J. Math. Oxford Ser. (2) 16 (1965), 193-232.
  11. A. Fröhlich, Galois module structure of algebraic integers, Ergeb. Math. Grenzgeb. 3, Vol. 1, Springer, 1983.
  12. H.-W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959), 119-149.
  13. G. Lettl, The ring of integers of an abelian number field, ibid. 404 (1990), 162-170.
  14. G. Lettl, Note on the Galois module structure of quadratic extensions, Colloq. Math. 67 (1994), 15-19.
  15. I. Reiner, Maximal Orders, London Math. Soc. Monographs 5, Academic Press, 1975.
  16. K. W. Roggenkamp and M. J. Taylor, Group rings and class groups, DMV-Sem. 18, Birkhäuser, 1992.
  17. M. J. Taylor, On the Galois module structure of rings of integers of wild, abelian extensions, J. London Math. Soc. 52 (1995), 73-87.
Acta Arithmetica
1998/85/3
Export to PBN, Opens in new tab
Pages:
235-248
Main language of publication
English
Received
1997-07-14
Published
1998
Exact and natural sciences