{"paper":{"title":"Adapted bases of Kisin modules and Serre weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hui Gao","submitted_at":"2015-05-11T15:13:14Z","abstract_excerpt":"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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02664","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}