Ramification groups of local fields with imperfect residue class fields (Q687522)

Let \(L/F\) be a finite Galois extension of complete discrete valuation fields, \(v_ L\) be the surjective discrete valuation of rank 1 on \(L\). There is Zariski-Samuel's filtration on \(G=\text{Gal}(L/F)\): \[ G=H_ 0\supset G_ 0\supset H_ 1\supset G_ 1\supset\dots \] where \(G_ i=\{\sigma\in G\): \(v_ L(\alpha)\geq 0 \Rightarrow v_ L(\sigma\alpha- \alpha)\geq i+1\}\), \(H_ i=\{\sigma\in G\): \(v_ L(\alpha)\geq 1\Rightarrow v_ L(\sigma\alpha-\alpha)\geq i+1\}\). Elementary properties of the filtration in the case of imperfect residue fields are listed in the paper.