Geodesic
The Maximal p-Extension of a Local Field
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 398-402

Voir la notice de l'article provenant de la source Cambridge University Press

1. Let k denote a local field, that is, a complete discrete-valued field with perfect residue class field . Let G denote the Galois group of the maximal separable algebraic extension M of k, and let g denote the corresponding object over . For a given prime integer p, let G(p) denote the Galois group of the maximal p-extension of k. The dimensions of the cohomology groups considered as vector spaces over the prime field Z/p Z, are equal, respectively, to the rank and the relation rank of the pro-p-group G(p); see [4; 9]. These dimensions are well known in many cases, especially when k is finite [6; 3; (Hoechsmann) 2, pp. 297-304], but also when k has characteristic p, or when k contains a primitive pth root of unity [4, p. 205]. 
Marshall, Murray A. The Maximal p-Extension of a Local Field. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 398-402. doi: 10.4153/CJM-1971-041-8
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