Galois cohomology revisited

We recast the Galois cohomology of the variety $V$ over a number field $k$ in terms of the K-theory of a $C^{\ast }$-algebra ${\mathcal{A}}_V$ connected to $V$. It is proved that $V$ is isomorphic to $V^{\mathrm{\prime }}$ over $k$ (algebraic closure of $k$, resp.) if and only if ${\mathcal{A}}_V$ is isomorphic (Morita equivalent, resp.) to ${\mathcal{A}}_{V^{\mathrm{\prime }}}$. In particular, the Morita equivalent $C^{\ast }$-algebras ${\mathcal{A}}_V$ parametrize twists of the variety $V$. The case of rational elliptic curves is considered in detail.