# Some counter-examples in the theory of the Galois module structure of wild extensions

Annales de l'institut Fourier (1980)

- Volume: 30, Issue: 3, page 1-9
- ISSN: 0373-0956

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topWilson, Stephen M. J.. "Some counter-examples in the theory of the Galois module structure of wild extensions." Annales de l'institut Fourier 30.3 (1980): 1-9. <http://eudml.org/doc/74460>.

@article{Wilson1980,

abstract = {Considering the ring of integers in a number field as a $\{\bf Z\}\Gamma $-module (where $\Gamma $ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.},

author = {Wilson, Stephen M. J.},

journal = {Annales de l'institut Fourier},

keywords = {Galois module structure; wild extensions; ring of integers; maximal order; twisted group rings},

language = {eng},

number = {3},

pages = {1-9},

publisher = {Association des Annales de l'Institut Fourier},

title = {Some counter-examples in the theory of the Galois module structure of wild extensions},

url = {http://eudml.org/doc/74460},

volume = {30},

year = {1980},

}

TY - JOUR

AU - Wilson, Stephen M. J.

TI - Some counter-examples in the theory of the Galois module structure of wild extensions

JO - Annales de l'institut Fourier

PY - 1980

PB - Association des Annales de l'Institut Fourier

VL - 30

IS - 3

SP - 1

EP - 9

AB - Considering the ring of integers in a number field as a ${\bf Z}\Gamma $-module (where $\Gamma $ is a galois group of the field), one hoped to prove useful theorems about the extension of this module to a module or a lattice over a maximal order. In this paper it is show that it could be difficult to obtain, in this way, parameters which are independent of the choice of the maximal order. Several lemmas about twisted group rings are required in the proof.

LA - eng

KW - Galois module structure; wild extensions; ring of integers; maximal order; twisted group rings

UR - http://eudml.org/doc/74460

ER -

## References

top- [1] E. ARTIN and J. TATE, Class Field Theory, Benjamin, New York, 1967. Zbl0176.33504
- [2] J. COUGNARD, Un Contre-exemple à une conjecture de J. Martinet, in 'Algebraic Number Fields', ed. Fröhlich, Acad. Press, New York, 1977. Zbl0358.12006MR56 #5494
- [3] J. COUGNARD, Une propriété de l'anneau des entiers des extensions galoisiennes non-abéliennes de degré pq des rationnels, to appear in Compositio Mathematica. Zbl0431.12005
- [4] A. FROHLICH, Locally free modules over arithmetic orders, J. Reine Angew. Math., 274/275 (1975), 112-138. Zbl0316.12013MR51 #12794
- [5] A. FROHLICH, Galois Module Structure, in Algebraic Number Fields, ed. Fröhlich, Acad. Press 1977. Zbl0346.12006MR56 #5496
- [6] I.N. ROSEN, Representations of twisted group rings, Thesis, Princeton University, 1963.
- [7] S.M.J. WILSON, K-Theory for twisted group rings, Proc. London Math. Soc., (3) 29 (1974), 257-271. Zbl0317.16012MR52 #8192

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