Soit une extension abélienne de corps -adiques, et soit l’anneau de valuation de . Nous étudions les idéaux de l’anneau de valuation de comme représentations entières du groupe de Galois . À supposer que soit absolument non ramifiée nous utilisons les techniques de la théorie de la factorisabilité pour examiner quels idéaux sont isomorphes à un -ordre dans l’algèbre du groupe . Nous obtenons de nouveaux résultats généraux et aussi explicites.
Let be an abelian extension of -adic fields, and let denote the valuation ring of . We study ideals of the valuation ring of as integral representations of the Galois group . Assuming is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an -order in the group algebra . We obtain several general and also explicit new results.
@article{AIF_1991__41_2_393_0, author = {Burns, David J.}, title = {Factorisability and wildly ramified {Galois} extensions}, journal = {Annales de l'Institut Fourier}, pages = {393--430}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {41}, number = {2}, year = {1991}, doi = {10.5802/aif.1259}, mrnumber = {92m:11135}, zbl = {0727.11048}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1259/} }
TY - JOUR AU - Burns, David J. TI - Factorisability and wildly ramified Galois extensions JO - Annales de l'Institut Fourier PY - 1991 SP - 393 EP - 430 VL - 41 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.1259/ DO - 10.5802/aif.1259 LA - en ID - AIF_1991__41_2_393_0 ER -
Burns, David J. Factorisability and wildly ramified Galois extensions. Annales de l'Institut Fourier, Tome 41 (1991) no. 2, pp. 393-430. doi : 10.5802/aif.1259. http://archive.numdam.org/articles/10.5802/aif.1259/
[1] Arithmétique d'une extension à groupe d'inertie cyclique, Ann. Inst. Fourier, 28, 4 (1978), 17-44. | Numdam | MR | Zbl
,[2] A propos du genre de l'anneau des entiers d'une extension, Publications Math. Sc. Besançon, (1979-1980), 1-9. | MR | Zbl
,[3] Factorisability, group lattices and Galois module structure, J. of Algebra, 134 (1990), 257-270. | Zbl
,[4] Canonical factorisability and a variant of Martinet's conjecture, to appear in J. London Math. Soc., (1991). | MR | Zbl
,[5] Factorizability, Grothendieck groups and Galois module structure, preprint, 1989.
and ,[6] Algebraic Number Theory, Proc. Brighton Symp., 1965, Academic Press, London, 1967. | Zbl
and (eds),[7] Elliptic functions and rings of integers, Progress in Mathematics, Volume 66, Birkhäuser Boston-Basel-Stuttgart, 1987. | MR | Zbl
and ,[8] A survey of recent work on the square root of the inverse different, Proceedings of the Journées Arithmétique 1989 at Luminy. | Numdam | Zbl
,[9] Sur les idéaux d'une extension cyclique de degré premier d'un corps local, C.R. Acad. Sc. Paris, 276 Série A (1973), 1483-1486. | MR | Zbl
,[10] Groupes de ramification et représentations d'Artin, Ann. Scient. Éc. Norm. Sup., 4e série, 4 (1971), 337-392. | Numdam | MR | Zbl
,[11] Invariants for modules over commutative separable orders, Quart. J. Math. Oxford, 16 (1965), 193-232. | MR | Zbl
,[12] Module defect and factorisability, Illinois J. Math., 32, 3 (1988), 407-421. | MR | Zbl
,[13] L-values at zero and multiplicative Galois module structure (also Galois Gauss sums and additive Galois module structure), J. reine und angew. Math., 397 (1989), 42-99. | MR | Zbl
,[14] On normal integral bases of local fields, J. of Algebra, 98 (1986), 197-199. | MR | Zbl
,[15] Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. reine und angew. Math., 201 (1959), 119-149. | MR | Zbl
,[16] Monomial representations and Galois module structure, Ph. D. Thesis, King's College, University of London, 1979.
,[17] Maximal Orders, Academic Press, London, 1975. | MR | Zbl
,[18] Corps Locaux, Hermann, Paris, 1962. | MR | Zbl
,[19] Iwasawa theory, factorisability and the Galois module structure of units, to appear. | Zbl
,[20] Induced representations and projective modules, Ann. of Math., 71 (1960), 552-578. | MR | Zbl
,[21] Normal bases in Galois extensions of number fields, Nagoya J., 34 (1969), 153-167. | MR | Zbl
,[22] Galois cohomology of Ambiguous Ideals, J. Number Theory, 1 (1969), 11-15. | MR | Zbl
,[23] Extensions with identical wild ramification, Sém. de Théorie des Nombres, Université de Bordeaux I, (1980-1981). | Zbl
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