On cohomology of Witt vectors of algebraic integers and a conjecture of Hesselholt

Let \(K\) be a complete discrete valued field of characteristic zero with residue field \(k_K\) of characteristic \(p > 0\). Let \(L/K\) be a finite Galois extension with the Galois group \(G\) and suppose that the induced extension of residue fields \(k_L/k_K\) is separable. In his paper, Hessel...

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Bibliographic Details
Published in:arXiv.org 2010-11
Main Authors: Hogadi, Amit, Pisolkar, Supriya
Format: Article
Language:English
Subjects:
Homology
Integers
Mathematical analysis
Vectors (mathematics)
Online Access:Get full text
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Summary:Let \(K\) be a complete discrete valued field of characteristic zero with residue field \(k_K\) of characteristic \(p > 0\). Let \(L/K\) be a finite Galois extension with the Galois group \(G\) and suppose that the induced extension of residue fields \(k_L/k_K\) is separable. In his paper, Hesselholt conjectured that \(H^1(G,W(\sO_L))\) is zero, where \(\sO_L\) is the ring of integers of \(L\) and \(W(\sO_L)\) is the Witt ring of \(\sO_L\) w.r.t. the prime \(p\). He partially proved this conjecture for a large class of extensions. In this paper, we prove Hesselholt's conjecture for all Galois extensions.
ISSN:2331-8422