Galois module structure of Milnor K-theory mod ps in characteristic p
Abstract
Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s in N, we determine KmE/psKmE as a (Z/psZ)[Gal(E/F)]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero.
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