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

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

2010-11-15

arxiv.org/abs/1011.3350v1

Mathematics

Number Theory

10 pages

Scientific paper

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.

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