### Galois cohomology of Witt vectors of algebraic integers

Let L/K be finite Galois extension of complete discrete valuation
fields of mixed characteristic with Galois group G and suppose that
the induced extension of residue fields is separable. It is well-known
that the group H^{1}(G,*O*_{L}) is zero if and
only if the extension L/K is tamely ramified. We show, however, that
the pro-abelian group H^{1}(G,W.(*O*_{L})) is
zero also for many wildly ramified extensions. Here
W.(*O*_{L}) is the pro-ring of Witt vectors in
*O*_{L}. We conjecture that this
pro-abelian group is zero for all Galois extensions L/K with separable
residue extension.
Lars Hesselholt <larsh@math.mit.edu>