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The main results are obtained by establishing an $R=\\mathbb{T}$-type result over the $\\mathrm{GL}_2(\\mathbb{Q}_p)$-ordinary families considered by"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.07372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-17T07:47:38Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"bd016b722f69425652dbf1a5043ca654f82fae35c93ad3b9c4a8c7d7bd4f7b67","abstract_canon_sha256":"475ab19a4abeff39c0a3cddb1ebc2dfd027afa11c1d06e66d2bf3c5f91eda266"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:22.456804Z","signature_b64":"THi+cvXh2GAAz0JNQArYuk8DfjQaeixU6F8BlEo7NJl2FV0E7ykcFT/ZNQgwQvK6/Vsx6Z9Q6bmdStlSkxA9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29c4ee7a0f09fec44ef0c76a754171ff9e00e2f554caac0ddf670e0455ad716a","last_reissued_at":"2026-05-17T23:40:22.456178Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:22.456178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathrm{GL}_2(\\mathbb{Q}_p)$-ordinary families and automorphy lifting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Yiwen Ding","submitted_at":"2019-07-17T07:47:38Z","abstract_excerpt":"We prove automorphy lifting results for certain essentially conjugate self-dual $p$-adic Galois representations $\\rho$ over CM imaginary fields $F$, which satisfy in particular that $p$ splits in $F$, and that the restriction of $\\rho$ on any decomposition group above $p$ is reducible with all the Jordan-H\\\"older factors of dimension at most $2$. 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