{"id":"https://openalex.org/W4377145804","doi":"https://doi.org/10.48550/arxiv.2305.11026","title":"Prosaic Abelian Varieties Bad at One Prime","display_name":"Prosaic Abelian Varieties Bad at One Prime","publication_year":2023,"publication_date":"2023-05-18","ids":{"openalex":"https://openalex.org/W4377145804","doi":"https://doi.org/10.48550/arxiv.2305.11026"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2305.11026","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.11026","pdf_url":"https://arxiv.org/pdf/2305.11026","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2305.11026","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022549197","display_name":"Armand Brumer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121847817","display_name":"The Graduate Center, CUNY","ror":"https://ror.org/00awd9g61","country_code":"US","type":"education","lineage":["https://openalex.org/I121847817"]},{"id":"https://openalex.org/I164389053","display_name":"Fordham University","ror":"https://ror.org/03qnxaf80","country_code":"US","type":"education","lineage":["https://openalex.org/I164389053"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brumer, Armand","raw_affiliation_strings":["Department of Mathematics , Fordham University , Bronx , NY 10458 , USA","Department of Mathematics , The Graduate Center of CUNY , New York , NY 10016 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Fordham University , Bronx , NY 10458 , USA","institution_ids":["https://openalex.org/I164389053"]},{"raw_affiliation_string":"Department of Mathematics , The Graduate Center of CUNY , New York , NY 10016 , USA","institution_ids":["https://openalex.org/I121847817"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088403731","display_name":"Kenneth L. Kramer","orcid":"https://orcid.org/0009-0003-0668-7595","observed_orcids":["https://orcid.org/0009-0003-0668-7595","https://orcid.org/0000-0002-5930-1612"]},"institutions":[{"id":"https://openalex.org/I111455621","display_name":"Queens College, CUNY","ror":"https://ror.org/03v8adn41","country_code":"US","type":"education","lineage":["https://openalex.org/I111455621"]},{"id":"https://openalex.org/I164389053","display_name":"Fordham University","ror":"https://ror.org/03qnxaf80","country_code":"US","type":"education","lineage":["https://openalex.org/I164389053"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kramer, Kenneth","raw_affiliation_strings":["Department of Mathematics , Fordham University , Bronx , NY 10458 , USA","Department of Mathematics , Queens College (CUNY) , Flushing , NY 11367 , USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Fordham University , Bronx , NY 10458 , USA","institution_ids":["https://openalex.org/I164389053"]},{"raw_affiliation_string":"Department of Mathematics , Queens College (CUNY) , Flushing , NY 11367 , USA;","institution_ids":["https://openalex.org/I111455621"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.7764000296592712,"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":0.7764000296592712,"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":0.21889999508857727,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/imaginary-quadratic-fields","display_name":"imaginary quadratic fields","score":0.6620000004768372},{"id":"https://openalex.org/keywords/isogenies","display_name":"isogenies","score":0.6079999804496765},{"id":"https://openalex.org/keywords/hasse-invariant","display_name":"Hasse invariant","score":0.4000000059604645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7734990119934082},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7532826662063599},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.597771406173706},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5322843194007874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49354612827301025},{"id":"https://openalex.org/C46709022","wikidata":"https://www.wikidata.org/wiki/Q318751","display_name":"Abelian variety","level":3,"score":0.48168906569480896},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.48146119713783264},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.4744618535041809},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4563513398170471},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.43884438276290894},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4300463795661926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3227594196796417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1381916105747223},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2305.11026","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.11026","pdf_url":"https://arxiv.org/pdf/2305.11026","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2305.11026","doi":"https://doi.org/10.48550/arxiv.2305.11026","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2305.11026","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2305.11026","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.11026","pdf_url":"https://arxiv.org/pdf/2305.11026","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309102","display_name":"City University of New York","ror":"https://ror.org/00453a208"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377145804.pdf","grobid_xml":"https://content.openalex.org/works/W4377145804.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2109426261","https://openalex.org/W7155496818","https://openalex.org/W3087456758","https://openalex.org/W571188762","https://openalex.org/W7100873438","https://openalex.org/W2949896387","https://openalex.org/W1978401138","https://openalex.org/W1562041956","https://openalex.org/W4394646178","https://openalex.org/W2008205914"],"abstract_inverted_index":{"We":[0,58,101,125],"say":[1],"that":[2,77,103,118,128],"an":[3,60],"abelian":[4,47,114],"variety":[5,115],"$A_{/\\mathbf":[6],"Q}$":[7],"of":[8,26,32,49,68,73,123],"dimension":[9],"$g$":[10],"is":[11,16,79,96,110,120],"{\\em":[12],"prosaic}":[13],"if":[14,104,145],"it":[15],"semistable,":[17],"with":[18,71,81,138,157],"good":[19],"reduction":[20,83],"at":[21,84,99],"2":[22,70],"and":[23,54,94,132],"its":[24],"points":[25,74],"order":[27],"$2$":[28],"generate":[29],"a":[30,111,121],"$2$-extension":[31],"${\\mathbf":[33,66,112],"Q}$.":[34],"For":[35],"$p":[36,90],"\\equiv":[37,91,140,159],"1":[38,92,142,161],"\\bmod{8}$,":[39],"let":[40,55],"$M_u$":[41],"be":[42],"the":[43,135,154],"maximal":[44],"2-primary":[45],"unramified":[46],"extension":[48],"$K":[50],"=":[51],"{\\mathbf":[52],"Q}(\\sqrt{-p})$":[53],"$h_2":[56],"=[M_u:K]$.":[57],"construct":[59],"indecomposable":[61],"group":[62],"scheme":[63],"$\u039e_p$":[64],"over":[65],"Z}[\\frac{1}{p}]$":[67],"exponent":[69],"field":[72],"$M_u$.":[75],"Assume":[76],"$A$":[78,95],"prosaic,":[80],"bad":[82],"only":[85],"one":[86],"prime":[87],"$p$.":[88,100],"Then":[89],"\\bmod{8}$":[93],"totally":[97],"toroidal":[98],"prove":[102],"End":[105],"$A={\\mathbf":[106],"Z}$,":[107],"then":[108,151],"there":[109],"Q}$-isogenous":[113],"$B$":[116],"such":[117],"$B[2]$":[119],"subquotient":[122],"$\u039e_p$.":[124],"thereby":[126],"show":[127],"$2g+2":[129],"\\le":[130,149],"h_2$":[131],"$p$":[133,152],"has":[134,153],"form":[136,155],"$a^2+16b^2$,":[137],"$a+4b":[139],"\\pm":[141,160],"\\bmod{8}$.":[143,162],"Moreover,":[144],"$2g":[146],"+":[147],"4":[148],"h_2$,":[150],"$a^2+64b^2$,":[156],"$a":[158]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2023-05-21T00:00:00"}