Galois module structure of Milnor $K$-theory in characteristic $p$
Ganesh Bhandari, Nicole Lemire, Jan Minac and John Swallow
Let $E$ be a cyclic extension of degree $p^n$ of a field $F$ of characteristic $p$. We determine $k_mE$, the Milnor $K$-groups modulo $p$, as ${\mathbb F}_p[{\rm Gal}(E/F)]$-modules for all $m\in {\mathbb N}$.