Galois module structure of the integers in wildly ramified cyclic extensions (Q1323858)

This paper is concerned with the Galois module structure of the ring of integers in totally ramified cyclic extensions, \(L/K\) of local fields whose characteristic is zero, \([L:K]= p^ m\), \(m\) arbitrary and \(p\) an odd prime. Under a restriction on the first ramification number, the structure of the ring of integers of \(L\) is described in terms of explicit indecomposable \(\mathbb{Z}_ p [G]\)-modules, \(G\) denoting the Galois group and \(\mathbb{Z}_ p\), the ring of \(p\)-adic integers.