{"paper":{"title":"Isotriviality and the space of morphisms on projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"Alon Levy, Anupam Bhatnagar","submitted_at":"2013-03-26T20:07:03Z","abstract_excerpt":"Let $K=k(C)$ be the function field of a smooth projective curve $C$ over an infinite field $k$, let $X$ be a projective variety over $k$. We prove two results. First, we show with some conditions that a $K$-morphism $\\phi: X_K \\to X_K$ of degree at least two is isotrivial if and only if $\\phi$ has potential good reduction at all places $v$ of $K$. Second, let $(X,\\phi), (Y,\\psi)$ be dynamical systems where $X,Y$ are defined over $k$ and $g:X_{K} \\to Y_{K}$ a dominant $K$-morphism, such that $g \\circ \\phi = \\psi \\circ g$. We show under certain conditions that if $\\phi$ is defined over $k$, then"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6646","kind":"arxiv","version":2},"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"}