Geodesic
On reductions of families of crystalline Galois representations
Documenta mathematica, Tome 15 (2010), pp. 873-938
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Let Kf​ be the finite unramified extension of Qp​ of degree f and E any finite large enough coefficient field containing Kf​. We construct analytic families of étale (φ,Γ)-modules which give rise to families of crystalline E-representations of the absolute Galois group GKf​​ of Kf​. For any irreducible effective two-dimensional crystalline E-representation of GKf​​ with labeled Hodge-Tate weights 0,−ki​τi​​ induced from a crystalline character of GK2f​​, we construct an infinite family of crystalline E -representations of GKf​​ of the same Hodge-Tate type which contains it. As an application, we compute the semisimplified mod p reductions of the members of each such family.
DOI : 10.4171/dm/317
Classification : 11F80, 11F85
Mots-clés : gamma)−modules, wach modules, (φ, reductions of crystalline Galois representations 
@article{10_4171_dm_317,
     author = {Gerasimos Dousmanis},
     title = {On reductions of families of crystalline {Galois} representations},
     journal = {Documenta mathematica},
     pages = {873--938},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/317},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/317/}
}
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Gerasimos Dousmanis. On reductions of families of crystalline Galois representations. Documenta mathematica, Tome 15 (2010), pp. 873-938. doi: 10.4171/dm/317

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