{"id":"W2891600716","doi":"10.1007/978-3-319-97379-1_15","title":"Explicit Arithmetic on Abelian Varieties","year":2018,"lang":"en","type":"book-chapter","venue":"Springer proceedings in mathematics & statistics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Abelian group; Variety (cybernetics); Abelian variety; Arithmetic of abelian varieties; Line bundle; Algebra over a field; Elementary abelian group; Projective variety; Rank of an abelian group; Euler's formula; Pure 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001523045,0.001170015,0.001490675,0.0008278096,0.0002103755,0.0002276675,0.0009104176,0.0008562509,0.002544826],"category_scores_gemma":[0.001752185,0.001154908,0.0002074222,0.0001606132,0.0004298682,0.0001373271,0.0003887437,0.001452966,0.001474609],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003169407,"about_ca_system_score_gemma":0.0001117074,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000333555,"about_ca_topic_score_gemma":0.000008650273,"domain_scores_codex":[0.9952838,0.00001366059,0.001624645,0.0009644552,0.001252655,0.0008608038],"domain_scores_gemma":[0.9959062,0.001391279,0.001161156,0.0007468456,0.0005537597,0.0002407181],"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":[0.00003656823,0.0002407724,0.000009987223,0.002794547,0.0001681868,0.00005864648,0.004056283,2.731954e-7,0.00001556118,0.9769763,0.0149066,0.0007362863],"study_design_scores_gemma":[0.0004371052,0.0003004491,0.000008823115,0.00189259,0.000268373,0.00003648076,0.0004956931,0.000160007,0.0002634673,0.9718313,0.02317955,0.001126157],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.002000392,0.00015041,0.02284139,0.00009349643,0.0007700631,0.001480489,0.0003259146,0.0004361284,0.9719017],"genre_scores_gemma":[0.003025092,0.000329119,0.3944022,0.0002450925,0.0008969415,0.000129501,0.00003883327,0.0007063361,0.6002269],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.3716748,"threshold_uncertainty_score":0.9993029,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03706086785097078,"score_gpt":0.2807863859565731,"score_spread":0.2437255181056023,"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."}}