{"id":"W4386722096","doi":"10.1016/j.aim.2025.110746","title":"Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's conjecture for zero-cycles","year":2025,"lang":"en","type":"preprint","venue":"Advances in Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"European Research Council; Institute of Sacred Music; Centre de Recherches Mathématiques; National Science Foundation","keywords":"Mathematics; Zero (linguistics); Algebraically closed field; Abelian group; Conjecture; Genus; Elliptic curve; Pure mathematics; Abelian variety; Kernel (algebra); Isogeny; Hyperelliptic curve; Product (mathematics); Image (mathematics); Algebra over a field; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001278179,0.001397099,0.001335143,0.006410478,0.003555216,0.005147641,0.001831596,0.002718174,0.01027137],"category_scores_gemma":[0.007843356,0.0006666855,0.001199074,0.005372711,0.005406049,0.007950535,0.004322424,0.00434117,0.000920027],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002637027,"about_ca_system_score_gemma":0.0008727338,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003340492,"about_ca_topic_score_gemma":0.002372432,"domain_scores_codex":[0.9993224,0.0002185541,0.00003623954,0.0001485007,0.0001463972,0.0001278878],"domain_scores_gemma":[0.9977417,0.001198263,0.0002455421,0.0002233276,0.0002727253,0.0003185562],"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":[0.00003767639,0.00002909382,0.0004866256,0.00003914837,0.000005740545,0.00009205858,0.0003636497,0.001286537,0.0002641363,0.9911282,0.001227549,0.005039675],"study_design_scores_gemma":[0.000009019037,0.000007315968,0.0001857104,0.00001874936,0.000005037892,0.00005444614,0.0002100697,0.003151934,0.0001556656,0.9943093,0.001883209,0.000009557669],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6276228,0.008712527,0.08485546,0.0146505,0.001373006,0.0001170536,0.0003652837,0.0004788521,0.2618245],"genre_scores_gemma":[0.955085,0.002816062,0.01175736,0.0005061844,0.0009436063,0.00007085117,0.0003167462,0.0001012811,0.028403],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01027137,"threshold_uncertainty_score":0.03436118,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03581341100601895,"score_gpt":0.3391053711848583,"score_spread":0.3032919601788394,"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."}}