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Let $K$ be a complete discrete valuation field of characteristic zero withresidue field $k_K$ of characteristic $p>0$. Let $L/K$ be a finite Galoisextension with Galois group $G=\Gal(L/K)$ and suppose that the inducedextension of residue fields $k_L/k_K$ is separable. Let $\mathbb{W}_n(\cdot)$denote the ring of $p$-typical Witt vectors of length $n$. Hesselholtconjectured that the pro-abelian group$\{H^1(G,\mathbb{W}_n(\mathcal{O}_L))\}_{n\geq 1}$ is isomorphic to zero.Hogadi and Pisolkar have recently provided a proof of this conjecture. In thispaper, we provide an alternative proof of Hesselholt's conjecture which issimpler in several respects.

An Alternative Proof of Hesselholt's Conjecture on Galois Cohomology of Witt Vectors of Algebraic Integers