Semi-stable \(p\)-adic representations and Griffiths’ transversality. (Représentations \(p\)-adiques semi-stables et transversalité de Griffiths.) (French) Zbl 0883.11049

Breuil, Christophe

Math. Ann. 307, No. 2, 191-224 (1997).

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.

Reviewer: C.Breuil (Palaiseau)

MSC:

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

Keywords:

semi-stable \(p\)-adic representation; Frobenius operator; monodromy operator; filtered modules; Griffiths transversality