no. 3
Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2
Annales de l'Institut Fourier, Volume 45 (1995) no. 3, pp. 625-647.

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.

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.

@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},
     pages = {625--647},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {45},
     number = {3},
     year = {1995},
     doi = {10.5802/aif.1468},
     zbl = {0820.11070},
     mrnumber = {96d:11125},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1468/}
}
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Elder, Gove Griffith. Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^2$. Annales de l'Institut Fourier, Volume 45 (1995) no. 3, pp. 625-647. doi : 10.5802/aif.1468. https://aif.centre-mersenne.org/articles/10.5802/aif.1468/

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