In the theory of local fields we have the well-known filtration of unit groups. In this short paper we compute the first cohomology groups of unit gorups for a finite Galois extension of local fields. We show that these cohomology groups are closely related to the ramification indices.
On orthogonal systems of shifts of scaling function on local fields of positive characteristic
On the action of the Weil group on the l-adic cohomology of rigid spaces over local fields
Branches in the Bruhat-Tits tree for local fields of even characteristic
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