On the action of the Weil group on the l-adic cohomology of rigid spaces over local fields

Details On the action of the Weil group on the l-adic cohomology of rigid spaces over local fields On the action of the Weil group on the l-adic cohomology of rigid spaces over local fields

2005-08-25

arxiv.org/abs/math/0508509v2

Mathematics

Number Theory

11 pages, minor modifications

Scientific paper

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.

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