in this joint work with Charles De Clercq, we introduce an
algebraic gadget, which we call Omega powers. This gadget bears strong
similarities with a recent construction of Kaledin.It allows to lift
characteristic of to W(k)-modules of high p-primary torsion. It is some
sort of 'Witt functor for modules'. When k is finite, it is moreover
equipped with unexpected extra structure.
Combining it with an axiomatized form of Hilbert's Theorem 90, we can
prove very general Lifting Theorems for the cohomology of a class of
profinite groups- the 'smooth' profinite groups. When giving
applications, I will try to be as precise (and honest!) regarding how
close we are to achieving an effective proof of the Bloch-Kato
conjecture- proved by Rost, Suslin and Voevodsky.