Galois cohomology of Witt vectors of algebraic integers

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 H¹(G,O_L) is zero if and only if the extension L/K is tamely ramified. We show, however, that the pro-abelian group H¹(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.

final.pdf [September 3, 2003]

Lars Hesselholt <larsh@math.nagoya-u.ac.jp>