On reductions of families of crystalline Galois representations
Let be the finite unramified extension of of degree and any finite large enough coefficient field containing We construct analytic families of étale -modules which give rise to families of crystalline -representations of the absolute Galois group of For any irreducible effective two-dimensional crystalline -representation of with labeled Hodge-Tate weights induced from a crystalline character of we construct an infinite family of crystalline -representations of of the same Hodge-Tate type which contains it. As an application, we compute the semisimplified mod reductions of the members of each such family.
Cite this article
Gerasimos Dousmanis, On reductions of families of crystalline Galois representations. Doc. Math. 15 (2010), pp. 873–938DOI 10.4171/DM/317