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.
Global Applications of relative (Phi-Gamma)-modules, I.
IOVITA, ADRIAN
2008
Abstract
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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