  We investigate the action of the Weil group on the compactly supported l-adic
etale cohomology groups of rigid spaces over a local field. We prove that the
alternating sum of the traces of the action is an integer and is independent of
l when either the rigid space is smooth or the characteristic of the base field
is equal to 0.
  We modify the argument of T. Saito to prove a result on l-independence for
nearby cycle cohomology, which leads to our l-independence result for smooth
rigid spaces.
  In the general case, we use the finiteness theorem of R. Huber, which
requires the restriction on the characteristic of the base field.
