{"paper":{"title":"On algebraically maximal valued fields that are not defectless","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Franz-Viktor Kuhlmann","submitted_at":"2026-01-08T12:18:11Z","abstract_excerpt":"An example originally given by F.~Delon shows the existence of an algebraically maximal discretely valued field of characteristic $p>0$ which admits purely inseparable extensions of degree $p^2$ with defect $p$. These extensions are not generated by a single element. Using a trick introduced in an earlier paper of the author, we construct algebraically maximal valued fields, of characteristic $p$ as well as of characteristic $0$, which admit separable extensions of degree $p^2$ with defect $p$. They are of rank 2 and it is an open question whether such examples having rank 1 exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.04872/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}