{"id":"https://openalex.org/W7220739555","doi":"https://doi.org/10.48550/arxiv.2610.04943","title":"Through the lens of the Eisenstein ideal","display_name":"Through the lens of the Eisenstein ideal","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220739555","doi":"https://doi.org/10.48550/arxiv.2610.04943"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04943","pdf_url":"https://arxiv.org/pdf/2610.04943","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/2610.04943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027865352","display_name":"Romyar T. Sharifi","orcid":"https://orcid.org/0000-0003-0675-1692","observed_orcids":["https://orcid.org/0000-0003-0675-1692"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sharifi, Romyar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5027865352"],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9848999977111816,"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"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9848999977111816,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.007499999832361937,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.0019000000320374966,"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/modular-curves","display_name":"modular curves","score":0.878000020980835},{"id":"https://openalex.org/keywords/cyclotomic-fields","display_name":"cyclotomic fields","score":0.8349999785423279},{"id":"https://openalex.org/keywords/modular-symbols","display_name":"modular symbols","score":0.8920000195503235},{"id":"https://openalex.org/keywords/euler-systems","display_name":"Euler systems","score":0.6809999942779541},{"id":"https://openalex.org/keywords/cyclotomic-units","display_name":"cyclotomic units","score":0.9909999966621399},{"id":"https://openalex.org/keywords/extension-classes","display_name":"extension classes","score":0.7269999980926514},{"id":"https://openalex.org/keywords/relative-cohomology","display_name":"relative cohomology","score":0.8930000066757202},{"id":"https://openalex.org/keywords/iwasawa-theory","display_name":"Iwasawa theory","score":0.7459999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8407999873161316},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7749000191688538},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4724999964237213},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C133835828","wikidata":"https://www.wikidata.org/wiki/Q1313257","display_name":"Eisenstein series","level":3,"score":0.44209998846054077},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42969998717308044},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.37040001153945923},{"id":"https://openalex.org/C38853081","wikidata":"https://www.wikidata.org/wiki/Q262370","display_name":"Eisenstein integer","level":3,"score":0.3571000099182129},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C2779467367","wikidata":"https://www.wikidata.org/wiki/Q863912","display_name":"Prime ideal","level":3,"score":0.3434999883174896},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.31299999356269836},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3034999966621399},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.25780001282691956}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04943","pdf_url":"https://arxiv.org/pdf/2610.04943","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.2610.04943","doi":"https://doi.org/10.48550/arxiv.2610.04943","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04943","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:2610.04943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04943","pdf_url":"https://arxiv.org/pdf/2610.04943","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220739555.pdf","grobid_xml":"https://content.openalex.org/works/W7220739555.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4391505411"],"related_works":["https://openalex.org/W3104675991","https://openalex.org/W2972138497","https://openalex.org/W2073082930","https://openalex.org/W2090346727","https://openalex.org/W4416892969","https://openalex.org/W1976369890","https://openalex.org/W2072134152","https://openalex.org/W2001274830","https://openalex.org/W3035459448","https://openalex.org/W2083103478"],"abstract_inverted_index":{"This":[0],"paper":[1],"exposits":[2],"relationships":[3],"between":[4,37],"the":[5,11,17,38,43,47,53,57,61,65,76,84,88,92,105,113,117,130],"geometry":[6],"of":[7,13,42,46,50,56,60,64,75,87,91,104,116,121,129,133,143],"modular":[8,96,144],"curves":[9,145],"and":[10,26,52,82,146],"arithmetic":[12],"cyclotomic":[14,67,134],"fields":[15],"through":[16],"Eisenstein":[18,44,89,114],"ideal.":[19],"For":[20],"an":[21,27,126],"integer":[22,68],"$N":[23],"\\ge":[24],"5$":[25],"odd":[28],"prime":[29],"$p$,":[30],"we":[31],"define":[32],"two":[33],"conjecturally":[34],"inverse":[35],"maps":[36],"real":[39,54],"part":[40,55],"$P$":[41,49,79,111],"reduction":[45,115],"homology":[48],"$X_1(N)$":[51],"$p$-part":[58],"$Y$":[59,81,109],"second":[62,106],"$K$-group":[63],"$N$th":[66],"ring.":[69],"We":[70,98,123],"recall":[71],"a":[72,100],"motivic":[73],"construction":[74,103,128],"map":[77,94,107],"from":[78,108],"to":[80,110],"describe":[83,147],"recent":[85],"proof":[86],"property":[90],"underlying":[93],"on":[95],"symbols.":[97],"provide":[99],"fully":[101],"equivariant":[102,127],"using":[112,136],"first":[118],"\u00e9tale":[119],"cohomology":[120,141],"$X_1(N)$.":[122],"then":[124],"explain":[125],"Euler":[131],"system":[132],"units":[135],"extension":[137],"classes":[138],"in":[139,150],"relative":[140],"groups":[142],"its":[148],"place":[149],"our":[151],"program.":[152]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
