Global applications of relative (phi-Gamma)-modules I

Details Global applications of relative (phi-Gamma)-modules I Global applications of relative (phi-Gamma)-modules I

2006-10-23

arxiv.org/abs/math/0610692v1

Mathematics

Number Theory

78 pages

Scientific paper

In this paper, given a smooth proper scheme X over a p-adic dvr and a p-power torsion etale local system L on it, we study a family of sheaves associated to the cohomology of local relative (Phi-Gamma)-modules of L and their cohomology. As applications we derive descriptions of the etale cohomology groups on the geometric generic fiber of X with values in L, as well as of their classical (Phi-Gamma)-modules, in terms of cohomology of the above mentioned sheaves.

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