{"paper":{"title":"Almost $C_p$ Galois representations and vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Marc Fontaine","submitted_at":"2018-05-08T09:02:03Z","abstract_excerpt":"Let $K$ be a finite extension of $\\mathbb{Q}_p$ and $G_K$ the absolute Galois group. Then $G_K$ acts on the fundamental curve $X$ of $p$-adic Hodge theory and we may consider the abelian category $\\mathcal{M}(G_K)$ of coherent $\\mathcal{O}_X$-modules equipped with a continuous and semi-linear action of $G_K$. An almost $C_p$-representation of $G_K$ is a $p$-adic Banach space $V$ equipped with a linear and continuous action of $G_K$ such that there exists $d\\in\\mathbb{N}$, two $G_K$-stable finite dimensional sub-$\\mathbb{Q}_p$-vector spaces $U_+$ of $V$, $U_-$ of $C_p^d$, and a $G_K$-equivarian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02905","kind":"arxiv","version":1},"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"}