{"id":"W2953134397","doi":"10.48550/arxiv.math/0404392","title":"Resolving G-torsors by abelian base extensions","year":2004,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; University of Alberta","funders":"","keywords":"Mathematics; Abelian group; Cohomological dimension; Surjective function; Abelian variety; Algebraically closed field; Field (mathematics); Algebraic number field; Field extension; Genus field; Projective variety; Pure mathematics; Conjecture; Algebraic number; Group (periodic table); Dimension (graph theory); Combinatorics; Abelian extension; Cohomology; Physics; 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":[0.001173711,0.0007853194,0.0005714145,0.001460088,0.001528568,0.002875912,0.0007935003,0.0009121582,0.005072297],"category_scores_gemma":[0.002149862,0.0004463584,0.0007743163,0.000754102,0.003926188,0.00559159,0.007257475,0.002226652,0.000590232],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001021507,"about_ca_system_score_gemma":0.0004627681,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005860502,"about_ca_topic_score_gemma":0.0005245326,"domain_scores_codex":[0.9990519,0.0001714258,0.00006591318,0.0002174908,0.0001981423,0.0002952061],"domain_scores_gemma":[0.9991032,0.0003290894,0.0001663948,0.0001297588,0.00004810693,0.0002234335],"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":[0.0001208661,0.0000696296,0.002074289,0.00007386699,0.00002737226,0.0009421797,0.001999637,0.002383661,0.004535686,0.9776461,0.0009215964,0.009205187],"study_design_scores_gemma":[0.00006885512,0.00009189947,0.001001234,0.0000359583,0.000031556,0.0007474888,0.001133711,0.006009458,0.006635514,0.9758013,0.008414684,0.00002820978],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9102425,0.000597435,0.04997954,0.0009134036,0.0001445164,0.00006004669,0.000146227,0.0002609807,0.03765535],"genre_scores_gemma":[0.9856228,0.0003097038,0.007626303,0.0001172539,0.0001242845,0.00002260087,0.0001312372,0.00003774682,0.006008101],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005072297,"threshold_uncertainty_score":0.01696855,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06672959389123223,"score_gpt":0.3047236913613874,"score_spread":0.2379940974701552,"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."}}