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Explicitly, this means that the lattice of the dual of $M$ is the dual of the lattice of $M$, i.e. the transposed of a Siegel matrix of $M$ is a Siegel matrix of the dual of $M$.\n  2. Let $n=r-1$. There is a 1 -- 1 correspondence between pure T-motives (all they are uniformizable), and lattices of rank $r$ in $C^n$ having dual (Corolla"},"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":"0711.1928","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-11-13T20:44:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"98d18914adfd57b5a31f633a93d9673d358d3ba08db631e30e3de4ba02ba493c","abstract_canon_sha256":"6058c8d5a8d4647602fb6a3fa0b3c915c4cd5d3028bc502977f8d7c9f45f88f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:44.692476Z","signature_b64":"X8SL9fIzF4NMm0ABtGigpLsJVoZl/iltopaMDHws7HrCGliTuclpI0EJPyDcpvFyV5qE//UFKRqBZjQVJF66Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d6e998eebdaab16a3c718bf34785f8f9e68621065f197daf9cfd18da41316b1","last_reissued_at":"2026-05-17T23:54:44.691848Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:44.691848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Duality of Anderson T-motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"A. Grishkov, D. Logachev","submitted_at":"2007-11-13T20:44:02Z","abstract_excerpt":"Let $M$ be a T-motive. We introduce the notion of duality for $M$. Main results of the paper (we consider uniformizable $M$ over $F_q[T]$ of rank $r$, dimension $n$, whose nilpotent operator $N$ is 0):\n  1. Algebraic duality implies analytic duality (Theorem 5). Explicitly, this means that the lattice of the dual of $M$ is the dual of the lattice of $M$, i.e. the transposed of a Siegel matrix of $M$ is a Siegel matrix of the dual of $M$.\n  2. Let $n=r-1$. There is a 1 -- 1 correspondence between pure T-motives (all they are uniformizable), and lattices of rank $r$ in $C^n$ having dual (Corolla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1928","kind":"arxiv","version":7},"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":"0711.1928","created_at":"2026-05-17T23:54:44.691965+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.1928v7","created_at":"2026-05-17T23:54:44.691965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.1928","created_at":"2026-05-17T23:54:44.691965+00:00"},{"alias_kind":"pith_short_12","alias_value":"JVXJTDXL3KVR","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"JVXJTDXL3KVRNI6H","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"JVXJTDXL","created_at":"2026-05-18T12:25:55.427421+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/JVXJTDXL3KVRNI6HDC7TI6C7R6","json":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6.json","graph_json":"https://pith.science/api/pith-number/JVXJTDXL3KVRNI6HDC7TI6C7R6/graph.json","events_json":"https://pith.science/api/pith-number/JVXJTDXL3KVRNI6HDC7TI6C7R6/events.json","paper":"https://pith.science/paper/JVXJTDXL"},"agent_actions":{"view_html":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6","download_json":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6.json","view_paper":"https://pith.science/paper/JVXJTDXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.1928&json=true","fetch_graph":"https://pith.science/api/pith-number/JVXJTDXL3KVRNI6HDC7TI6C7R6/graph.json","fetch_events":"https://pith.science/api/pith-number/JVXJTDXL3KVRNI6HDC7TI6C7R6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6/action/storage_attestation","attest_author":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6/action/author_attestation","sign_citation":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6/action/citation_signature","submit_replication":"https://pith.science/pith/JVXJTDXL3KVRNI6HDC7TI6C7R6/action/replication_record"}},"created_at":"2026-05-17T23:54:44.691965+00:00","updated_at":"2026-05-17T23:54:44.691965+00:00"}