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An Alternative Proof of Hesselholt's Conjecture on Galois Cohomology of Witt Vectors of Algebraic Integers | | Wilson Ong
; | | Date: |
8 Aug 2011 | | Abstract: | Let $K$ be a complete discrete valuation field of characteristic zero with
residue field $k_K$ 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 $k_L/k_K$ is separable. Let $mathbb{W}_n(cdot)$
denote the ring of $p$-typical Witt vectors of length $n$. Hesselholt
conjectured that the pro-abelian group
${H^1(G,mathbb{W}_n(mathcal{O}_L))}_{ngeq 1}$ is isomorphic to zero.
Hogadi and Pisolkar have recently provided a somewhat lengthy proof of the
conjecture. In this paper, we provide a considerably shorter proof of
Hesselholt’s conjecture. | | Source: | arXiv, 1108.1744 | | Services: | Forum | Review | PDF | Favorites | |
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