{"id":"W4415951229","doi":"10.1215/00127094-2025-0016","title":"Abelian varieties not isogenous to Jacobians over global fields","year":2025,"lang":"","type":"article","venue":"Duke Mathematical Journal","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Abelian group; Abelian variety; Field (mathematics); Algebra over a field; Abelian variety of CM-type","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":[0.0009239787,0.001168702,0.001401425,0.004371372,0.003354448,0.005688579,0.00117504,0.001224236,0.009386762],"category_scores_gemma":[0.003086156,0.0007870833,0.0010115,0.001961165,0.005263111,0.008853315,0.003911874,0.003959259,0.001194096],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001441512,"about_ca_system_score_gemma":0.0006699018,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000748981,"about_ca_topic_score_gemma":0.0006566744,"domain_scores_codex":[0.998907,0.0001668745,0.00005175533,0.0002737121,0.0002562816,0.0003443779],"domain_scores_gemma":[0.9978231,0.0005736324,0.0003842401,0.0003077297,0.0002895005,0.0006217633],"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":[0.0001425111,0.0000704647,0.0006606271,0.00003570573,0.00001815531,0.0003337898,0.0005679523,0.0004262125,0.00162996,0.991964,0.0008365167,0.003314082],"study_design_scores_gemma":[0.00007755132,0.00009747117,0.001747583,0.00002205161,0.00003850578,0.0005100743,0.0005306252,0.001234608,0.001085954,0.9886451,0.005980229,0.00003034489],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8199366,0.0006488963,0.02005215,0.001135231,0.0008196867,0.00009960946,0.0002420837,0.0004146195,0.1566511],"genre_scores_gemma":[0.9691454,0.0003724653,0.002255993,0.0002024249,0.0004905339,0.00003493367,0.0002890217,0.0001356264,0.02707366],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009386762,"threshold_uncertainty_score":0.03140181,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02159008966626188,"score_gpt":0.3321565992620064,"score_spread":0.3105665095957446,"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."}}