An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors

Amit Hogadi¹ ; Supriya Pisolkar¹

¹ School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Colaba, Mumbai 400005, India

Acta Arithmetica, Tome 158 (2013) no. 2, pp. 165-171.

Résumé

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.

Détail

DOI : 10.4064/aa158-2-4

Keywords: finite galois extension complete discrete valued fields characteristic assume induced residue field extension k separable integer geq mathcal denote ring witt vectors length coefficients mathcal proabelian group mathcal mathbb zero equicharacteristic analogue hesselholts conjecture which proved before discrete valued fields mixed characteristic