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 the action of the Weil group on the l-adic cohomology of rigid spaces over local fields
Height of Some Automorphisms of Local Fields
Selberg Integral over Local Fields
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