On l-independence for the etale cohomology of rigid spaces over local fields

Details On l-independence for the etale cohomology of rigid spaces over local fields On l-independence for the etale cohomology of rigid spaces over local fields

2006-01-05

arxiv.org/abs/math/0601100v2

Mathematics

Algebraic Geometry

38 pages; revised version

Scientific paper

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.

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