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Suppose that the N\\'eron model $\\CA$ of $A$ over $S$ has a closed fibre $\\CA_s$, which is an abelian variety of $p$-rank 0. We show that under these assumptions the group $A(K^\\perf)/\\Tr_{K|k}(A)(k)$ is finitely generated. Here $K^\\perf=K^{p^{-\\infty}}$ is the maximal purely inseparable extension of $K$. This result implies that in some circumstances, the \"full\" Mordell-Lang conjecture, as well as a conjecture of Esnault"},"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":"1211.6943","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-29T15:10:19Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"39543f923ede720800b0798410df675e2f5191012209b42618886de9eaf488eb","abstract_canon_sha256":"03a0f7cfb1d52564bab6a80262b2f7f4f3148a23207a0587b00c433ae447e866"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:42.643452Z","signature_b64":"wLmg/O/ZhNyT5zAQ5v4vz/dsHX+r9Zh/HNoCfa1l/615O+VugcAS8iG3VGtMIyh0ZxwEw5j9MIvApPpEE3xGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68cad059fe551869016520d6b775054f012d435c185e60d2da5642f64855cc5a","last_reissued_at":"2026-05-18T03:39:42.642608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:42.642608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AG","authors_text":"Damian R\\\"ossler","submitted_at":"2012-11-29T15:10:19Z","abstract_excerpt":"Let $K$ be the function field of a smooth and proper curve $S$ over an algebraically closed field $k$ of characteristic $p>0$. Let $A$ be an ordinary abelian variety over $K$. Suppose that the N\\'eron model $\\CA$ of $A$ over $S$ has a closed fibre $\\CA_s$, which is an abelian variety of $p$-rank 0. We show that under these assumptions the group $A(K^\\perf)/\\Tr_{K|k}(A)(k)$ is finitely generated. Here $K^\\perf=K^{p^{-\\infty}}$ is the maximal purely inseparable extension of $K$. 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