Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2
Elder, Gove Griffith
Annales de l'Institut Fourier, Tome 45 (1995), p. 625-647 / Harvested from Numdam
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Pour n’importe quelle extension cyclique ramifiée de degré p 2 des corps locaux L/K qui sont des extensions finies du corps des nombres p-adiques, nous proposons une description de la ℤ p [ Gal (L/K)]-structure de chaque idéal fractionnaire de L utilisant les 4p+1 modules indécomposables sur ℤ p [ Gal (L/K)] que Heller et Reiner ont classifié. Les exposants sont entièrement déterminés par les invariants de la ramification.

For L/K, any totally ramified cyclic extension of degree p 2 of local fields which are finite extensions of the field of p-adic numbers, we describe the ℤ p [ Gal (L/K)]-module structure of each fractional ideal of L explicitly in terms of the 4p+1 indecomposable ℤ p [ Gal (L/K)]-modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

@article{AIF_1995__45_3_625_0,
     author = {Elder, Gove Griffith},
     title = {Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^2$},
     journal = {Annales de l'Institut Fourier},
     volume = {45},
     year = {1995},
     pages = {625-647},
     doi = {10.5802/aif.1468},
     mrnumber = {96d:11125},
     zbl = {0820.11070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1995__45_3_625_0}
}

Elder, Gove Griffith. Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^2$. Annales de l'Institut Fourier, Tome 45 (1995) pp. 625-647. doi : 10.5802/aif.1468. http://gdmltest.u-ga.fr/item/AIF_1995__45_3_625_0/

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