2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74949We compute the reduction modulo $p$ of 2-dimensional crystalline representations whose Hodge-Tate weights are 0 and $k-1$ with $k \in \{p+2,...,2p-1\}$.typos corrected, one new result added (theorem 2.2.5)Number TheoryAlgebraic Geometry11Ftext