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We associate to a finitely generated module $D$ over the Fontaine ring over $o $ endowed with a semilinear \\'etale action of the monoid $T_{+} $ (acting on the Fontaine ring via $\\alpha$), a $G(\\mathbb Q_{p})$-equivariant sheaf of $o$-modules on the compact space $G(\\mathbb Q_{p})/P(\\mathbb Q_{p})$. Our construction generalizes the representation $D\\boxtimes \\mathbb P^{1} $ of $ GL(2,\\mathbb"},"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":"1206.1125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-06T06:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"1c192f613ec899169bf1c91ab0744e70edb37e3451ee8173d9518c7e58ea09ea","abstract_canon_sha256":"2a7e0c98b758dac6527387714f2f5a13408aaf9ef03039a5688738fd8d3593b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:02.588501Z","signature_b64":"lWytzVYjjxffwK6RBEJEaAtp4pnSCHD5WX2NnruQjPs490Hzw0ikSLj4r7KiCQ/yfgJwlxPg/Yn6IEHmessDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caf4b47dc71f6af7c521cdfe91492fb72dfd6b5492edfcaaf2919b81c94ddb41","last_reissued_at":"2026-05-18T02:31:02.588038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:02.588038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From \\'etale $P_{+}$-representations to $G$-equivariant sheaves on $G/P$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gergely Zabradi, Marie-France Vigneras, Peter Schneider","submitted_at":"2012-06-06T06:16:52Z","abstract_excerpt":"Let $K/\\mathbb Q_{p}$ be a finite extension with ring of integers $o$, let $G$ be a connected reductive split $\\mathbb Q_{p}$-group of Borel subgroup $P=TN$ and let $\\alpha$ be a simple root of $T$ in $N$. 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Our construction generalizes the representation $D\\boxtimes \\mathbb P^{1} $ of $ GL(2,\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1125","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.1125","created_at":"2026-05-18T02:31:02.588102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.1125v1","created_at":"2026-05-18T02:31:02.588102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1125","created_at":"2026-05-18T02:31:02.588102+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZL2LI7OHD5VP","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZL2LI7OHD5VPPRJB","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZL2LI7OH","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4","json":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4.json","graph_json":"https://pith.science/api/pith-number/ZL2LI7OHD5VPPRJBZX7JCSJPW4/graph.json","events_json":"https://pith.science/api/pith-number/ZL2LI7OHD5VPPRJBZX7JCSJPW4/events.json","paper":"https://pith.science/paper/ZL2LI7OH"},"agent_actions":{"view_html":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4","download_json":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4.json","view_paper":"https://pith.science/paper/ZL2LI7OH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.1125&json=true","fetch_graph":"https://pith.science/api/pith-number/ZL2LI7OHD5VPPRJBZX7JCSJPW4/graph.json","fetch_events":"https://pith.science/api/pith-number/ZL2LI7OHD5VPPRJBZX7JCSJPW4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4/action/storage_attestation","attest_author":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4/action/author_attestation","sign_citation":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4/action/citation_signature","submit_replication":"https://pith.science/pith/ZL2LI7OHD5VPPRJBZX7JCSJPW4/action/replication_record"}},"created_at":"2026-05-18T02:31:02.588102+00:00","updated_at":"2026-05-18T02:31:02.588102+00:00"}