On the Galois structure of the square root of the codifferent

D. Burns

Journal de théorie des nombres de Bordeaux (1991)

  • Volume: 3, Issue: 1, page 73-92
  • ISSN: 1246-7405

Abstract

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Let L be a finite abelian extension of ℚ , with 𝒪 L the ring of algebraic integers of L . We investigate the Galois structure of the unique fractional 𝒪 L -ideal which (if it exists) is unimodular with respect to the trace form of L / ℚ .

How to cite

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Burns, D.. "On the Galois structure of the square root of the codifferent." Journal de théorie des nombres de Bordeaux 3.1 (1991): 73-92. <http://eudml.org/doc/93537>.

@article{Burns1991,
abstract = {Let $L$ be a finite abelian extension of $\mathbb \{Q\}$, with $\mathcal \{O\}_L$ the ring of algebraic integers of $L$. We investigate the Galois structure of the unique fractional $\mathcal \{O\}_L$ -ideal which (if it exists) is unimodular with respect to the trace form of $L/ \mathbb \{Q\}$.},
author = {Burns, D.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {corps de nombres; formes quadratiques entières; fractional ideal; maximal order; finite abelian extension; trace form; Galois structure},
language = {eng},
number = {1},
pages = {73-92},
publisher = {Université Bordeaux I},
title = {On the Galois structure of the square root of the codifferent},
url = {http://eudml.org/doc/93537},
volume = {3},
year = {1991},
}

TY - JOUR
AU - Burns, D.
TI - On the Galois structure of the square root of the codifferent
JO - Journal de théorie des nombres de Bordeaux
PY - 1991
PB - Université Bordeaux I
VL - 3
IS - 1
SP - 73
EP - 92
AB - Let $L$ be a finite abelian extension of $\mathbb {Q}$, with $\mathcal {O}_L$ the ring of algebraic integers of $L$. We investigate the Galois structure of the unique fractional $\mathcal {O}_L$ -ideal which (if it exists) is unimodular with respect to the trace form of $L/ \mathbb {Q}$.
LA - eng
KW - corps de nombres; formes quadratiques entières; fractional ideal; maximal order; finite abelian extension; trace form; Galois structure
UR - http://eudml.org/doc/93537
ER -

References

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  2. [2] C. Bachoc, Sur la structure hermitienne de la racine carrée de la codifférente, to appear. MR1242610
  3. [3] C. Bachoc et B. Erez, Forme trace et ramification sauvage, Proc. London Math. Soc.61 (1990), 209-226. Zbl0708.11059MR1063045
  4. [4] A-M. Bergé, Arithmétique d'une extension galoisienne à groupe d'inertie cyclique, Ann. Inst. Fourier28 (1978), 17-44. Zbl0377.12009MR513880
  5. [5] A-M. Bergé, A propos du genre des entiers d'une extension, Publications Math. Sc. Besançon (1979- 1980), 1-9. Zbl0472.12006
  6. [6] D. Burns, Canonical factorisability and a variant of Martinet's conjecture, to appear in J. London Math. Soc. (1991). Zbl0751.11053
  7. [7] B. Erez, Structure galoasienne et forme trace, Thèse, Genève1987; see also J. Algebra118 (1988), 438-446. Zbl0663.12015MR969683
  8. [8] B. Erez, A survey of recent work on the square root of the inverse different, to appear in the proceedings of the Journées arithmétiques, Luminy (1989). Zbl0752.11048MR1144319
  9. [9] B. Erez and M.J. Taylor, Hermitian modules in Galois extensions of number fields and Adams operations, to appear. Zbl0756.11035
  10. [10] A. Fröhlich, Galois module structure of algebraic integers, Ergebnisse der Mathematik 3. Folge, Bd. 1Berlin: Springer (1983). Zbl0501.12012MR717033
  11. [11] S. Lang, Algebraic Number Theory, Graduate Texts in Mathematics 110Springer-Verlag, Heidelberg (1986). Zbl0601.12001MR1282723
  12. [12] H.W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. reine und angew. Math201 (1959), 119-149. Zbl0098.03403MR108479
  13. [13] G. Lettl, The ring of integers of an abelian number field, J. reine und angew. Math.400 (1990), 162-170. Zbl0703.11060MR1037435
  14. [14] I. Reiner, Maximal Orders, Academic Press, London (1975). Zbl0305.16001MR1972204
  15. [15] J-P. Serre, Corps Locaux, Hermann, Paris, (1962). MR354618

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