In this paper, given a smooth proper scheme $X$ over a $p$-adic DVR and a $p$-power torsion \''etale local system ${\bf L}$ on it, we study a family of sheaves associated to the cohomology of local, relative $(\phi,\Gamma)$-modules of ${\bf L}$ and their cohomology. As applications we derive descriptions of the \''etale cohomology groups on the geometric generic fiber of $X$ with values in ${\bf L}$, 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 / F. Andreatta, A. Iovita. - In: ASTÉRISQUE. - ISSN 0303-1179. - 319:319(2008), pp. 339-420.

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

F. Andreatta
Primo
;
2008

Abstract

In this paper, given a smooth proper scheme $X$ over a $p$-adic DVR and a $p$-power torsion \''etale local system ${\bf L}$ on it, we study a family of sheaves associated to the cohomology of local, relative $(\phi,\Gamma)$-modules of ${\bf L}$ and their cohomology. As applications we derive descriptions of the \''etale cohomology groups on the geometric generic fiber of $X$ with values in ${\bf L}$, as well as of their classical $(\phi,\Gamma)$-modules, in terms of cohomology of the above mentioned sheaves.
(phi, Gamma)-modules ; etale cohomology ; Fontaine sheaves ; Grothendieck topologies ; comparison isomorphisms
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/53854
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