Galois module structure of Milnor K-theory mod p^s in characteristic p

Jan Minac, Andrew Schultz, John Swallow

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 K_mE/p^sK_mE as a (Z/p^sZ)[Gal(E/F)]-module. We also provide examp…