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In the case n=1 we introduce an algebraic stack equipped with a morphism to $Disp_1^G$. We conjecture that if G=GL(d) then the new stack is canonically isomorphic to the reduction modulo p of the stack of 1-truncated Barsotti-Tate groups of height d and dimension d', where d' depends on the action of $G_m$ on GL(d).\n  We also discuss how to defin"},"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":"2304.11709","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-04-23T17:56:32Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"450020e823bd9f1c11590c14b0f1066150b67b45ef8d0f72a8065180ee1f5378","abstract_canon_sha256":"c29e4bd8a3ccd4c2e6014f6757a585d659b774b75e1091eade50851ffb7b554c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:07.779056Z","signature_b64":"trtW3BjudpX4hTjR62UWQnEjCS5l0li1lk3ERaCYByg9oeCFwA80Dpbjts6BZqf2Ufnw0nTZLoX47XATvb1/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f10c70724f5d9e73c02d10c90f99c9170291df7d973bc44acc73ba9037cf3eb","last_reissued_at":"2026-07-05T09:52:07.778485Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:07.778485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Shimurian generalizations of the stack $BT_1\\otimes F_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Vladimir Drinfeld","submitted_at":"2023-04-23T17:56:32Z","abstract_excerpt":"Let G be a smooth group scheme over $F_p$ equipped with a $G_m$-action such that all weights of $G_m$ on the Lie algebra of G are not greater than 1. 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We conjecture that if G=GL(d) then the new stack is canonically isomorphic to the reduction modulo p of the stack of 1-truncated Barsotti-Tate groups of height d and dimension d', where d' depends on the action of $G_m$ on GL(d).\n  We also discuss how to defin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.11709","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.11709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2304.11709","created_at":"2026-07-05T09:52:07.778571+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.11709v4","created_at":"2026-07-05T09:52:07.778571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.11709","created_at":"2026-07-05T09:52:07.778571+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4IMOBZE6XM6","created_at":"2026-07-05T09:52:07.778571+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4IMOBZE6XM6OPAC","created_at":"2026-07-05T09:52:07.778571+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4IMOBZE","created_at":"2026-07-05T09:52:07.778571+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.10226","citing_title":"An algebraicity conjecture of Drinfeld and the moduli of $p$-divisible groups","ref_index":23,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF","json":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF.json","graph_json":"https://pith.science/api/pith-number/J4IMOBZE6XM6OPAC2EGJB6M4SF/graph.json","events_json":"https://pith.science/api/pith-number/J4IMOBZE6XM6OPAC2EGJB6M4SF/events.json","paper":"https://pith.science/paper/J4IMOBZE"},"agent_actions":{"view_html":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF","download_json":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF.json","view_paper":"https://pith.science/paper/J4IMOBZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.11709&json=true","fetch_graph":"https://pith.science/api/pith-number/J4IMOBZE6XM6OPAC2EGJB6M4SF/graph.json","fetch_events":"https://pith.science/api/pith-number/J4IMOBZE6XM6OPAC2EGJB6M4SF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF/action/storage_attestation","attest_author":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF/action/author_attestation","sign_citation":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF/action/citation_signature","submit_replication":"https://pith.science/pith/J4IMOBZE6XM6OPAC2EGJB6M4SF/action/replication_record"}},"created_at":"2026-07-05T09:52:07.778571+00:00","updated_at":"2026-07-05T09:52:07.778571+00:00"}