{"id":"W2093311528","doi":"10.4153/cmb-2005-002-x","title":"On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves","year":2005,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":53,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University; Fields Institute for Research in Mathematical Sciences","funders":"Queen's University","keywords":"Mathematics; Surjective function; Galois module; Elliptic curve; Division (mathematics); Multiplication (music); Prime (order theory); Complex multiplication; Pure mathematics; Schoof's algorithm; Integer (computer science); Galois group; Discrete mathematics; Arithmetic; Combinatorics; Quarter period","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"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":[0.00395614,0.0007944851,0.0009847094,0.003650396,0.002771675,0.006453949,0.001338709,0.001135331,0.004430592],"category_scores_gemma":[0.01559566,0.0008884332,0.0008147881,0.001469879,0.007830453,0.009186425,0.007239813,0.004128799,0.0005801002],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00163921,"about_ca_system_score_gemma":0.0006340127,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006753966,"about_ca_topic_score_gemma":0.0004706036,"domain_scores_codex":[0.9971426,0.0006780665,0.00014839,0.00065381,0.0007287625,0.0006483528],"domain_scores_gemma":[0.9824762,0.009784195,0.001877124,0.001857826,0.001176038,0.002828619],"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":[0.0001763534,0.00006066503,0.002506174,0.00005551302,0.00001628741,0.0003023343,0.001011842,0.001859255,0.00184533,0.9868277,0.0002970003,0.005041462],"study_design_scores_gemma":[0.00003506769,0.0001456465,0.003230912,0.00008056215,0.00003587623,0.0005534129,0.0004601446,0.01345065,0.004294479,0.9756896,0.001952478,0.0000711869],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9239345,0.0005518591,0.04710417,0.000823207,0.00006537158,0.00002992972,0.0001288894,0.0001700354,0.02719205],"genre_scores_gemma":[0.9950835,0.0002431438,0.00224509,0.00005077572,0.000123956,0.00002064331,0.00009500205,0.00002685058,0.00211113],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006453949,"threshold_uncertainty_score":0.0209223,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02345731692727591,"score_gpt":0.2664764728080044,"score_spread":0.2430191558807285,"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."}}