Connes reformulates Weil's question <a href="http://www.alainconnes.org/docs/ramis.pdf" title="pdf">here</a> as: "Is there a non trivial Brauer theory of central simple algebras over $\mathbb{C}$ ?" and tells his solution of his reformulation in the context of a "cosmic galois group" in renormalization <a href="http://www.alainconnes.org/docs/imufinal.pdf" title="pdf">here</a>.