On reductions of families of crystalline Galois representations
Documenta mathematica, Tome 15 (2010), pp. 873-938.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: Let $K_f$ be the finite unramified extension of $\{Q}_p$ of degree $f$ and $E$ any finite large enough coefficient field containing $K_f.$ We construct analytic families of étale $(\varphi ,\Gamma )$-modules which give rise to families of crystalline $E$-representations of the absolute Galois group $G_{K_f}$ of $K_f.$ For any irreducible effective two-dimensional crystalline $E$-representation of $G_{K_f}$ with labeled Hodge-Tate weights ${0,-k_i}_{\tau _i}$ induced from a crystalline character of $G_{K_{2f}},$ we construct an infinite family of crystalline $E$ -representations of $G_{K_f}$ 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.
Classification : 11F80, 11F85
Mots-clés : wach modules, $(\varphi $, gamma)$-modules$, reductions of crystalline Galois representations 
@article{DOCMA_2010__15__a7,
     author = {Dousmanis, Gerasimos},
     title = {On reductions of families of crystalline {Galois} representations},
     journal = {Documenta mathematica},
     pages = {873--938},
     publisher = {mathdoc},
     volume = {15},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a7/}
}
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Dousmanis, Gerasimos. On reductions of families of crystalline Galois representations. Documenta mathematica, Tome 15 (2010), pp. 873-938. https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a7/