{"paper":{"title":"On the Northcott property and other properties related to polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Martin Widmer, Sara Checcoli","submitted_at":"2011-11-21T23:26:02Z","abstract_excerpt":"We prove that if $K/\\mathbb{Q}$ is a Galois extension of finite exponent and $K^{(d)}$ is the compositum of all extensions of $K$ of degree at most $d$, then $K^{(d)}$ has the Bogomolov property and the maximal abelian subextension of $K^{(d)}/\\mathbb{Q}$ has the Northcott property.\n  Moreover, we prove that given any sequence of finite solvable groups $\\{G_m\\}_m$ there exists a sequence of Galois extensions $\\{K_m\\}_m$ with $\\text{Gal}(K_m/\\mathbb{Q})=G_m$ such that the compositum of the fields $K_m$ has the Northcott property. In particular we provide examples of fields with the Northcott pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5060","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"}