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Given a Drinfeld module $\\Phi:{\\mathbb F}[t] \\to \\operatorname{End}_K({\\mathbb G}_a)$ over $K$ and a positive integer $g$ we regard both $K^g$ and ${\\mathbf A}_K^g$ as $\\Phi({\\mathbb F}_p[t])$-modules under the diagonal action induced by $\\Phi$. For $\\Gamma \\subseteq K^g$ a finitely generated $\\Phi(\\F_p[t])$-submodule and an affine subvariety $X \\su"},"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":"1012.1825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-08T18:51:18Z","cross_cats_sorted":["math.AG","math.LO"],"title_canon_sha256":"224b34a88ea247f33d4b608032189321c009206d90fa838a682ab4e19045e811","abstract_canon_sha256":"859179857569cf4965171beebbba8dac0e4359ae5b08f8b836707c92cb4fa78a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:51.191581Z","signature_b64":"JUhvhOR7mc4bkLCs9xNn+pxobC4c3/hT9AUCbGMTAgLL9x0hb3/IO2IFVGdTuehWPik8JPdU5b+llbOvZjiCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6938c42d17d695f3a5f50764782062d207b7a8452d21769565596aa1106e2156","last_reissued_at":"2026-05-18T04:33:51.191057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:51.191057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic equations on the adelic closure of a Drinfeld module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Thomas Scanlon","submitted_at":"2010-12-08T18:51:18Z","abstract_excerpt":"Let $k$ be a field of positive characteristic and $K = k(V)$ a function field of a variety $V$ over $k$ and let ${\\mathbf A}_K$ be a ring of ad\\'{e}les of $K$ with respect to a cofinite set of the places on $K$ corresponding to the divisors on $V$. Given a Drinfeld module $\\Phi:{\\mathbb F}[t] \\to \\operatorname{End}_K({\\mathbb G}_a)$ over $K$ and a positive integer $g$ we regard both $K^g$ and ${\\mathbf A}_K^g$ as $\\Phi({\\mathbb F}_p[t])$-modules under the diagonal action induced by $\\Phi$. For $\\Gamma \\subseteq K^g$ a finitely generated $\\Phi(\\F_p[t])$-submodule and an affine subvariety $X \\su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1825","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":"1012.1825","created_at":"2026-05-18T04:33:51.191133+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.1825v1","created_at":"2026-05-18T04:33:51.191133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1825","created_at":"2026-05-18T04:33:51.191133+00:00"},{"alias_kind":"pith_short_12","alias_value":"NE4MILIX22K7","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"NE4MILIX22K7HJPV","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"NE4MILIX","created_at":"2026-05-18T12:26:10.704358+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/NE4MILIX22K7HJPVA5SHQIDC2I","json":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I.json","graph_json":"https://pith.science/api/pith-number/NE4MILIX22K7HJPVA5SHQIDC2I/graph.json","events_json":"https://pith.science/api/pith-number/NE4MILIX22K7HJPVA5SHQIDC2I/events.json","paper":"https://pith.science/paper/NE4MILIX"},"agent_actions":{"view_html":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I","download_json":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I.json","view_paper":"https://pith.science/paper/NE4MILIX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.1825&json=true","fetch_graph":"https://pith.science/api/pith-number/NE4MILIX22K7HJPVA5SHQIDC2I/graph.json","fetch_events":"https://pith.science/api/pith-number/NE4MILIX22K7HJPVA5SHQIDC2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I/action/storage_attestation","attest_author":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I/action/author_attestation","sign_citation":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I/action/citation_signature","submit_replication":"https://pith.science/pith/NE4MILIX22K7HJPVA5SHQIDC2I/action/replication_record"}},"created_at":"2026-05-18T04:33:51.191133+00:00","updated_at":"2026-05-18T04:33:51.191133+00:00"}