  We use the theory of Condensed Mathematics to build a condensed cohomology
theory for the Weil group of a $p$-adic field. The cohomology groups are proved
to be locally compact abelian groups of finite ranks in some special cases.
This allows us to enlarge the local Tate Duality to a more general category of
non-necessarily discrete coefficients, where it takes the form of a Pontryagin
duality between locally compact abelian groups.
