Let K be a complete discrete valuation field of characteristic zero with
residue field kKβ of characteristic p>0. Let L/K be a finite Galois
extension with Galois group G=\Gal(L/K) and suppose that the induced
extension of residue fields kLβ/kKβ is separable. Let Wnβ(β )
denote the ring of p-typical Witt vectors of length n. Hesselholt
conjectured that the pro-abelian group
{H1(G,Wnβ(OLβ))}nβ₯1β is isomorphic to zero.
Hogadi and Pisolkar have recently provided a proof of this conjecture. In this
paper, we provide an alternative proof of Hesselholt's conjecture which is
simpler in several respects.Comment: 3 pages; added references, changed Remark 2.1 to a lemma and proof,
updated abstrac