Abstract
Let K be an unramified extension of {mathbb {Q}}_p and rho :G_K rightarrow {text {GL}}_n(overline{{mathbb {Z}}}_p) a crystalline representation. If the Hodge–Tate weights of rho differ by at most p then we show that these weights are contained in a natural collection of weights depending only on the restriction to inertia of {overline{rho }} = rho otimes _{overline{{mathbb {Z}}}_p} overline{{mathbb {F}}}_p. Our methods involve the study of a full subcategory of p-torsion Breuil–Kisin modules which we view as extending Fontaine–Laffaille theory to filtrations of length p.
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