{"paper":{"title":"$p$-adic Hodge theory in rigid analytic families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rebecca Bellovin","submitted_at":"2013-06-24T17:32:56Z","abstract_excerpt":"We study the functors $\\D_{\\B_\\ast}(V)$, where $\\B_\\ast$ is one of Fontaine's period rings and $V$ is a family of Galois representations with coefficients in an affinoid algebra $A$. We show that $\\D_{\\HT}(V)=\\oplus_{i\\in\\Z}(\\D_{\\Sen}(V)\\cdot t^i)^{\\Gamma_K}$, $\\D_{\\dR}(V)=\\D_{\\dif}(V)^{\\Gamma_K}$, and $\\D_{\\cris}(V)=\\D_{\\rig}(V)[1/t]^{\\Gamma_K}$, generalizing results of Sen, Fontaine, and Berger. The modules $\\D_{\\HT}(V)$ and $\\D_{\\dR}(V)$ are coherent sheaves on $\\Sp(A)$, and $\\Sp(A)$ is stratified by the ranks of submodules $\\D_{\\HT}^{[a,b]}(V)$ and $\\D_{\\dR}^{[a,b]}(V)$ of \"periods with Ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5685","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"}