An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors
Volume 158 / 2013
Acta Arithmetica 158 (2013), 165-171
MSC: Primary 11S25.
DOI: 10.4064/aa158-2-4
Abstract
Let $L/K$ be a finite Galois extension of complete discrete valued fields of characteristic $p$. Assume that the induced residue field extension $k_L/k_K$ is separable. For an integer $n\geq 0$, let $W_n(\mathcal O_L)$ denote the ring of Witt vectors of length $n$ with coefficients in $\mathcal O_L$. We show that the proabelian group $\{H^1(G,W_n(\mathcal O_L))\}_{n\in \mathbb N}$ is zero. This is an equicharacteristic analogue of Hesselholt's conjecture, which was proved before when the discrete valued fields are of mixed characteristic.
