{"id":"https://openalex.org/W7222917138","doi":"https://doi.org/10.48550/arxiv.2610.23430","title":"Brauer-Manin obstruction for symmetric powers","display_name":"Brauer-Manin obstruction for symmetric powers","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222917138","doi":"https://doi.org/10.48550/arxiv.2610.23430"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23430","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23430","pdf_url":"https://arxiv.org/pdf/2610.23430","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.23430","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159057984","display_name":"Yang Cao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cao, Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101686192","display_name":"Lin Zhou","orcid":"https://orcid.org/0009-0002-7002-3139","observed_orcids":["https://orcid.org/0009-0002-7002-3139"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9678000211715698,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9678000211715698,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.029500000178813934,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/brauer-manin-obstruction","display_name":"Brauer-Manin obstruction","score":1.0},{"id":"https://openalex.org/keywords/symmetric-powers","display_name":"symmetric powers","score":0.9620000123977661},{"id":"https://openalex.org/keywords/zero-cycles","display_name":"zero-cycles","score":0.8510000109672546},{"id":"https://openalex.org/keywords/weak-approximation","display_name":"weak approximation","score":0.9959999918937683},{"id":"https://openalex.org/keywords/brauer-group","display_name":"Brauer group","score":0.9409999847412109},{"id":"https://openalex.org/keywords/number-fields","display_name":"number fields","score":0.7049999833106995},{"id":"https://openalex.org/keywords/cohomological-obstructions","display_name":"cohomological obstructions","score":0.7419999837875366}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8400999903678894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5206000208854675},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3346000015735626},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23430","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23430","pdf_url":"https://arxiv.org/pdf/2610.23430","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.23430","doi":"https://doi.org/10.48550/arxiv.2610.23430","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23430","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.23430","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23430","pdf_url":"https://arxiv.org/pdf/2610.23430","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5089335471","display_name":null,"funder_award_id":"948066","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222917138.pdf","grobid_xml":"https://content.openalex.org/works/W7222917138.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7123606221","https://openalex.org/W7160928735"],"related_works":["https://openalex.org/W7123606221","https://openalex.org/W3017251479","https://openalex.org/W2963741040","https://openalex.org/W4392750009","https://openalex.org/W2962977045","https://openalex.org/W2151652950","https://openalex.org/W1628402740","https://openalex.org/W3123629209","https://openalex.org/W2749164610","https://openalex.org/W2111441656"],"abstract_inverted_index":{"For":[0],"a":[1,9,30,55,63],"quasi-projective":[2],"smooth":[3],"geometrically":[4],"integral":[5],"variety":[6],"$X$":[7],"over":[8],"number":[10],"field,":[11],"we":[12],"prove":[13],"that":[14],"the":[15,24,35],"Brauer-Manin":[16,32],"obstruction":[17,25,33,42],"for":[18,34,48,59,67],"its":[19],"symmetric":[20,36],"powers":[21,37],"coincides":[22],"with":[23],"coming":[26],"from":[27],"$X$.":[28,49],"As":[29],"consequence,":[31],"cannot":[38],"provide":[39],"new":[40],"cohomological":[41],"to":[43],"weak":[44],"approximation":[45],"of":[46],"zero-cycles":[47],"The":[50],"key":[51],"intermediate":[52],"ingredients":[53],"are":[54],"Dold-Thom":[56],"type":[57],"result":[58],"Brauer":[60],"groups":[61],"and":[62],"precise":[64],"descent":[65],"formula":[66],"adelic":[68],"points.":[69]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-20T00:00:00"}