{"paper":{"title":"Un th\\'eor\\`eme de l'application ouverte sur les corps valu\\'es alg\\'ebriquement clos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Laurent Moret-Bailly","submitted_at":"2010-10-02T14:48:09Z","abstract_excerpt":"Let K be an algebraically closed valued field, and let f:X--->Y be a universally open morphism of K-schemes of finite type. We show that the induced map on K-rational points is open for the topologies deduced from the absolute value of K.\n  ------\n  Soit K un corps valu\\'e alg\\'ebriquement clos, et soit f:X--->Y un morphisme universellement ouvert de K-sch\\'emas de type fini. On montre que l'application de X(K) dans Y(K) induite par f est ouverte pour les topologies d\\'eduites de la valeur absolue sur K."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0341","kind":"arxiv","version":3},"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"}