New ramification breaks and additive Galois structure
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 87-107.

Quels invariants d’une p-extension galoisienne de corps local L/K (de corps résiduel de charactéristique p et groupe de Galois G) déterminent la structure des idéaux de L en tant que modules sur l’anneau de groupe p [G], p l’anneau des entiers p-adiques ? Nous considérons cette question dans le cadre des extensions abéliennes élémentaires, bien que nous considérions aussi brièvement des extensions cycliques. Pour un groupe abélien élémentaire G, nous proposons et étudions un nouveau groupe (dans l’anneau de groupe 𝔽 q [G]𝔽 q est le corps résiduel) ainsi que ses filtrations de ramification.

Which invariants of a Galois p-extension of local number fields L/K (residue field of char p, and Galois group G) determine the structure of the ideals in L as modules over the group ring p [G], p the p-adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups G, we propose and study a new group (within the group ring 𝔽 q [G] where 𝔽 q is the residue field) and its resulting ramification filtrations.

@article{JTNB_2005__17_1_87_0,
     author = {Byott, Nigel P. and Elder, G. Griffith},
     title = {New ramification breaks and additive Galois structure},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {87--107},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {1},
     year = {2005},
     doi = {10.5802/jtnb.479},
     mrnumber = {2152213},
     zbl = {1162.11394},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.479/}
}
Byott, Nigel P.; Elder, G. Griffith. New ramification breaks and additive Galois structure. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 87-107. doi : 10.5802/jtnb.479. http://www.numdam.org/articles/10.5802/jtnb.479/

[1] M. V. Bondarko, Links between associated additive Galois modules and computation of H 1 for local formal group modules. J. Number Theory 101 (2003), 74–104. | MR 1979653 | Zbl 1037.11079

[2] N. P. Byott, G. G. Elder, Biquadratic extensions with one break. Can. Math. Bull. 45 (2002), 168–179. | MR 1904081 | Zbl 1033.11054

[3] G. G. Elder, Galois module structure of integers in wildly ramified cyclic extensions of degree p 2 . Ann. Inst. Fourier (Grenoble) 45 (1995), 625–647; errata ibid. 48 (1998), 609–610. | Numdam | MR 1340947 | Zbl 0820.11070

[4] G. G. Elder, Galois module structure of ambiguous ideals in biquadratic extensions. Can. J. Math. 50 (1998), 1007–1047. | MR 1650942 | Zbl 1015.11056

[5] G. G. Elder, On the Galois structure of the integers in cyclic extensions of local number fields. J. Théor. Nombres Bordeaux. 14 (2002), 113–149. | Numdam | MR 1925994 | Zbl 1026.11083

[6] G. G. Elder, The Galois module structure of ambiguous ideals in cyclic extensions of degree 8. To appear in the Proceedings of the International Algebraic Conference dedicated to the memory of Z. I. Borevich, Sept 17–23, 2002.

[7] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics: A Foundation for Computer Science. Addison Wesley, Reading MA 1989. | MR 1397498 | Zbl 0668.00003

[8] J. V. Kuzmin, Representations of finite groups by automorphisms of nilpotent near spaces and by automorphisms of nilpotent groups. Sibirsk. Mat. Ž. 13 (1972), 107–117. | MR 369505 | Zbl 0229.20007

[9] J-P. Serre, Local Fields. Springer-Verlag, New York, 1979. | MR 554237 | Zbl 0423.12016

[10] A. Weiss, Rigidity of p-adic p-torsion. Ann. of Math. (2) 127 (1988), 317–332. | MR 932300 | Zbl 0647.20007

[11] B. Wyman, Wildly ramified gamma extensions. Amer. J. Math. 91 (1969), 135–152. | MR 241386 | Zbl 0188.11003