Central simple algebras, Milnor $K$-theory and homogeneous spaces over complete discretely valued fields of dimension 2

Philippe Gille, Diego Izquierdo, Giancarlo Lucchini Arteche

Let $K$ be a complete discretely valued field with residue field $\bar{K}$ of dimension $1$ (not necessarily perfect). This occurs if and only if $K$ has dimension $2$. We prove the…