{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QZO4C7CMZXGDIQZEOBBUUIVQ7U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cfb1dc208d2d57b652b1ee8ef009ea36adb28bcf824b737a6611a7eb0b5004d7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-07-09T12:02:18Z","title_canon_sha256":"5c80070b91549bd3dfae6f5b75f7d27e8e6848f3d27527b37c8ac990554ee716"},"schema_version":"1.0","source":{"id":"1607.02602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02602","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02602v2","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02602","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"pith_short_12","alias_value":"QZO4C7CMZXGD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QZO4C7CMZXGDIQZE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QZO4C7CM","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:25649ce8a97fd867d7d3f0ca41e9711238baef8a951fa985b9e9301c9410b2d8","target":"graph","created_at":"2026-05-17T23:56:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study deformations of smooth mod $p$ representations (and their duals) of a $p$-adic reductive group $G$. Under some mild genericity condition, we prove that parabolic induction with respect to a parabolic subgroup $P=LN$ defines an isomorphism between the universal deformation rings of a supersingular representation $\\bar{\\sigma}$ of $L$ and of its parabolic induction $\\bar{\\pi}$. As a consequence, we show that every Banach lift of $\\bar{\\pi}$ is induced from a unique Banach lift of $\\bar{\\sigma}$.","authors_text":"Claus Sorensen, Julien Hauseux, Tobias Schmidt","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-07-09T12:02:18Z","title":"Deformation rings and parabolic induction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02602","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:856750a966c5cfb65431ee8f49cddbcfdcfb3f2ee9cc96d36d1bd729f9987c9a","target":"record","created_at":"2026-05-17T23:56:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cfb1dc208d2d57b652b1ee8ef009ea36adb28bcf824b737a6611a7eb0b5004d7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-07-09T12:02:18Z","title_canon_sha256":"5c80070b91549bd3dfae6f5b75f7d27e8e6848f3d27527b37c8ac990554ee716"},"schema_version":"1.0","source":{"id":"1607.02602","kind":"arxiv","version":2}},"canonical_sha256":"865dc17c4ccdcc34432470434a22b0fd13b78a4c3c0844341e642ae420fcf6c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"865dc17c4ccdcc34432470434a22b0fd13b78a4c3c0844341e642ae420fcf6c0","first_computed_at":"2026-05-17T23:56:56.143472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:56.143472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qxm6s4YW00WGSZQzrnXRuBiVmMaDwNxuCtan/F7/S5zvXu8RVRNRjejUr9w4b+y8wsf1CWknd7gl/B8Oq6YnDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:56.144251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:856750a966c5cfb65431ee8f49cddbcfdcfb3f2ee9cc96d36d1bd729f9987c9a","sha256:25649ce8a97fd867d7d3f0ca41e9711238baef8a951fa985b9e9301c9410b2d8"],"state_sha256":"c72cf28f30e825aada258cc98d6600464e31482e3285d618d3851c241bc4dcbb"}