{"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 $K$. This result implies that in some circumstances, the \"full\" Mordell-Lang conjecture, as well as a conjecture of Esnault"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6943","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"}