{"paper":{"title":"Une factorisation de la cohomologie compl\\'et\\'ee et du syst\\`eme de Beilinson-Kato","arxiv_id":"2104.09200","primary_cat":"math.NT","submitted_at":"2021-04-19T10:46:48+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":0.87,"id":"s0","own":true,"role":"result","text":"We show that the modular symbol $(0,\\infty)$, considered as an element of the dual of Emerton's completed cohomology, interpolates Kato's Euler system at classical points, and we deduce from this a factorisation of Beilinson-Kato's system as a product of two symbols $(0,\\infty)$ (an algebraic analog of Rankin's method).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.92,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.87,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.0}},{"i":1,"p":0.98,"id":"s1","own":true,"role":"method","text":"The proof uses the $p$-adic local Langlands correspondence for ${\\mathbf GL}_2({\\mathbf Q}_p)$ and Emerton's factorization of the completed cohomology of the tower of modular curves for which we provide a new proof resting upon the construction of a Kirillov model for the completed cohomology, and which we refine by imposing conditions at classical points; the existence of such a refinement is a manifestation of an analyticity property for $p$-adic periods of modular forms.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.89,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.98,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"We show that the modular symbol $(0,\\infty)$, considered as an element of the dual of Emerton's completed cohomology, interpolates Kato's Euler system at classical points, and we deduce from this a factorisation of Beilinson-Kato's system as a product of two symbols $(0,\\infty)$ (an algebraic analog of Rankin's method).","location":"abstract s0","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":2604,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.05,"states_limitation":0.08,"human_participants":0.01,"controlled_comparison":0.01,"randomized_assignment":0.01,"states_quantitative_result":0.03,"compares_with_prior_results":0.66,"mentions_code_or_data_availability":0.01},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.6,"text":"We show that the modular symbol $(0,\\infty)$, considered as an element of the dual of Emerton's completed cohomology, interpolates Kato's Euler system at classical points, and we deduce from this a factorisation of Beilinson-Kato's system as a product of two symbols $(0,\\infty)$ (an algebraic analog of Rankin's method).","location":"abstract s0"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":2,"sentences_in_abstract":2},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}