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Semi-stable $$p$$-adic representations and Griffiths’ transversality. (Représentations $$p$$-adiques semi-stables et transversalité de Griffiths.) (French) Zbl 0883.11049
Kato’s logarithmic interpretation of Fontaine’s ring $$B_{st}$$ has given birth to a “bigger” ring: $$\widehat{B_{st}}$$. We use this ring to define $$\widehat {B_{st}}$$-admissible $$p$$-adic representations and to show that they are just Fontaine’s semi-stable representations. To do this, we study the ring $$S$$ of Galois invariant elements of $$\widehat {B_{st}}$$ and we show an equivalence of categories between Fontaine’s category of filtered modules with Frobenius and monodromy and a category of filtered $$S$$-modules with Frobenius and monodromy satisfying Griffiths’ transversality condition.

##### MSC:
 11S20 Galois theory 14F20 Étale and other Grothendieck topologies and (co)homologies 14F30 $$p$$-adic cohomology, crystalline cohomology
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