Trivial integral Galois module structure of weakly ramified extensions of p-adic fields

Details Trivial integral Galois module structure of weakly ramified extensions of p-adic fields Trivial integral Galois module structure of weakly ramified extensions of p-adic fields

2012-04-10

arxiv.org/abs/1204.2133v1

Mathematics

Number Theory

6 pages, preliminary version

Scientific paper

Let p be a rational prime and let $K$ be a finite extension of Q_p. Let L be a finite Galois extension extension of K and let G=Gal(L/K). We say that L/K is weakly ramified if and only if its second ramification group is trivial. Let O_L be the valuation ring of L and let P_L be its maximal ideal. We show that if L/K is weakly ramified then P_L is free over the group ring O_K[G], and from this we deduce that if L/K is wildly and weakly ramified then O_L is free over its associated order in the group algebra K[G].

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