  We investigate the action of the Weil group on the compactly supported l-adic
cohomology groups of rigid spaces over local fields. We prove that every
eigenvalue of the action is a Weil number when either a rigid space is smooth
or the characteristic of the base field is equal to 0. Since a smooth rigid
space is locally isomorphic to the Raynaud generic fiber of an algebraizable
formal scheme, we can use the techniques of alterations and monodromy spectral
sequences in the smooth case. In the general case, we use the continuity
theorem of Huber, which requires the restriction on the characteristic of the
base field.
