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arXiv · 1505.02664

Adapted bases of Kisin modules and Serre weights

Hui Gao
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Abstract

Let $p>2$ be a prime. Let $K$ be a tamely ramified finite extension over $\mathbb Q_p$ with ramification index $e$, and let $G_K$ be the Galois group. We study Kisin modules attached to crystalline representations of $G_K$ whose labeled Hodge-Tate weights are relatively small (a sort of "$er\le p$" condition where $r$ is the maximal Hodge-Tate weight). In particular, we show that these Kisin modules admit "adapted bases". We then apply these results in the special case $e=2$ to study reductions and liftings of certain crystalline representations. As a consequence, we establish some new cases of weight part of Serre's conjectures (when $e=2$).

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Hui Gao. 2015-05-11. Adapted bases of Kisin modules and Serre weights. https://arxiv.org/abs/1505.02664

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