Bases normales relatives en caractéristique positive

Bruno Anglès

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 1, page 1-17
  • ISSN: 1246-7405

Abstract

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In this paper, we study the Galois module structure of the ring of integers of cyclotomic function fields in the tame case. We show that, in general, these rings are not free over the group ring if the genus of the base field is greater than 1 .

How to cite

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Anglès, Bruno. "Bases normales relatives en caractéristique positive." Journal de théorie des nombres de Bordeaux 14.1 (2002): 1-17. <http://eudml.org/doc/248921>.

@article{Anglès2002,
abstract = {Dans cet article, nous étudions la structure galoisienne des anneaux d’entiers des corps de fonctions cyclotomiques dans le cas modéré. Nous montrons qu’en général, si le corps de base est de genre plus grand que $1$, ces anneaux ne sont pas libres sur les anneaux de groupes considérés.},
author = {Anglès, Bruno},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {integral normal bases; tame ``cyclotomic'' extensions; rational function field},
language = {fre},
number = {1},
pages = {1-17},
publisher = {Université Bordeaux I},
title = {Bases normales relatives en caractéristique positive},
url = {http://eudml.org/doc/248921},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Anglès, Bruno
TI - Bases normales relatives en caractéristique positive
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 1
SP - 1
EP - 17
AB - Dans cet article, nous étudions la structure galoisienne des anneaux d’entiers des corps de fonctions cyclotomiques dans le cas modéré. Nous montrons qu’en général, si le corps de base est de genre plus grand que $1$, ces anneaux ne sont pas libres sur les anneaux de groupes considérés.
LA - fre
KW - integral normal bases; tame ``cyclotomic'' extensions; rational function field
UR - http://eudml.org/doc/248921
ER -

References

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  1. [1] B. Anglès, On the orthogonal of cyclotomic units in positive characteristic. J. Number Theory79 (1999), 258-283. Zbl1001.11046MR1728150
  2. [2] J. Brinkhuis, Galois modules and embedding problems. J. Reine Ang. Math, 346 (1984), 141-164. Zbl0525.12008MR727401
  3. [3] J. Brinkhuis, Normal integral bases and complex conjugation. J. Reine Ang. Math375/376 (1987), 157-166. Zbl0609.12009MR882295
  4. [4] R.J. Chapman, Carlitz modules and normal integral bases. J. London Math. Soc.44 (1991), 250-260. Zbl0749.11049MR1136438
  5. [5] J. Cougnard, Bases normales relatives dans certaines extensions cyclotomiques. J. Number Theory23 (1986), 336-346. Zbl0588.12003MR846963
  6. [6] J. Cougnard, Nouveaux exemples d'extensions relatives sans base normale. preprint 2001. 
  7. [7] A. Fröhlich, Galois module sructure of algebraic integers. Springer-Verlag, 1983. Zbl0501.12012MR717033
  8. [8] D. Goss, Basic structures of function field arithmetic. Springer-Verlag, 1996. Zbl0874.11004MR1423131
  9. [9] C. Greither, Relative integral normal bases in Q(ζp), J. Number Theory35 (1990), 180-193. Zbl0718.11053
  10. [10] C. Greither, D.R. Replogle, K. Rubin, A. Srivastav, Swan modules and Hilbert-Speiser number fields. J. Number Theory79 (1999), 164-173. Zbl0941.11044MR1718724
  11. [11] D. Hayes, Explicit class field theory for rational function fields. Trans. Amer. Math. soc.189 (1974), 77-91. Zbl0292.12018MR330106
  12. [12] J.T. Tate, Global class field theory. In Algebraic Number Theory, edited by J. W. S. Cassels and A. Frôhlich, Academic Press, 162-203, 1967. Zbl1179.11041MR220697
  13. [13] D. Thakur, Gauss sums for Fq [T]. Invent. Math.94 (1988), 105-112. Zbl0629.12014MR958591

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