{"id":"W1538184085","doi":"10.1090/s0002-9947-04-03463-4","title":"Value groups, residue fields, and bad places of rational function fields","year":2004,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":85,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Algebraic closure; Residue field; Separable space; Algebraic number; Residue (chemistry); Pure mathematics; Algebraic extension; Valuation (finance); Algebraic function; Rational function; Field (mathematics); Discrete mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001101516,0.000723829,0.0006007181,0.002954751,0.001581465,0.002922424,0.0005426805,0.0005476706,0.00202238],"category_scores_gemma":[0.001556314,0.0002523621,0.0007190963,0.001518757,0.005197254,0.006777736,0.002237549,0.001397535,0.0002803732],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008691032,"about_ca_system_score_gemma":0.000369062,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004222216,"about_ca_topic_score_gemma":0.0004237506,"domain_scores_codex":[0.9994959,0.00007964692,0.00003876143,0.0001017566,0.0001101793,0.000173751],"domain_scores_gemma":[0.998849,0.0004140473,0.0002454326,0.0001585719,0.00007345549,0.0002594647],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003605189,0.0001061622,0.01188358,0.0001270345,0.00003074433,0.0007456815,0.002050297,0.003812897,0.006911425,0.9442931,0.0007203041,0.02895829],"study_design_scores_gemma":[0.00004228025,0.0001494531,0.004508885,0.00007400908,0.00004810653,0.001042688,0.001575791,0.006450034,0.006127935,0.9710202,0.008908316,0.00005229639],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9589685,0.0005869555,0.02505194,0.0003982518,0.00003636176,0.00002803642,0.0001101423,0.00006158099,0.01475824],"genre_scores_gemma":[0.9897969,0.0003338039,0.006711635,0.00002974001,0.00006073393,0.00001677262,0.0001578583,0.00001233326,0.002880032],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002954751,"threshold_uncertainty_score":0.006765544,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01423645949972987,"score_gpt":0.2600219753759486,"score_spread":0.2457855158762187,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}