{"id":"https://openalex.org/W7214987241","doi":"https://doi.org/10.48550/arxiv.2609.37595","title":"Ax-Schanuel for the Drinfeld $j$-function","display_name":"Ax-Schanuel for the Drinfeld $j$-function","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214987241","doi":"https://doi.org/10.48550/arxiv.2609.37595"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37595","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37595","pdf_url":"https://arxiv.org/pdf/2609.37595","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055754292","display_name":"Gal Binyamini","orcid":"https://orcid.org/0000-0002-2714-4106","observed_orcids":["https://orcid.org/0000-0002-2714-4106"]},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Binyamini, Gal","raw_affiliation_strings":["Department of Mathematics , Weizmann Institute of Science , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Weizmann Institute of Science , Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130793496","display_name":"Dmitry Novikov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Novikov, Dmitry","raw_affiliation_strings":["Department of Mathematics , Weizmann Institute of Science , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Weizmann Institute of Science , Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088757222","display_name":"Francesco Maria Saettone","orcid":"https://orcid.org/0000-0002-2892-6978","observed_orcids":["https://orcid.org/0000-0002-2892-6978"]},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Saettone, Francesco Maria","raw_affiliation_strings":["Department of Mathematics , Weizmann Institute of Science , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Weizmann Institute of Science , Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I53964585"],"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":0.9761000275611877,"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":0.9761000275611877,"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":0.007199999876320362,"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/drinfeld-modular-curves","display_name":"Drinfeld modular curves","score":0.578000009059906},{"id":"https://openalex.org/keywords/positive-characteristic","display_name":"positive characteristic","score":0.7820000052452087},{"id":"https://openalex.org/keywords/differential-galois-theory","display_name":"differential Galois theory","score":0.7699999809265137},{"id":"https://openalex.org/keywords/foliations","display_name":"foliations","score":0.7990000247955322},{"id":"https://openalex.org/keywords/intersection-theory","display_name":"intersection theory","score":0.3070000112056732}],"concepts":[{"id":"https://openalex.org/C2777183706","wikidata":"https://www.wikidata.org/wiki/Q630771","display_name":"Subvariety","level":3,"score":0.9337000250816345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375999927520752},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5370000004768372},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4867999851703644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4424999952316284},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3986000120639801},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3926999866962433},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C2777573902","wikidata":"https://www.wikidata.org/wiki/Q1491747","display_name":"Galois connection","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37595","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37595","pdf_url":"https://arxiv.org/pdf/2609.37595","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.2609.37595","doi":"https://doi.org/10.48550/arxiv.2609.37595","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37595","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:2609.37595","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37595","pdf_url":"https://arxiv.org/pdf/2609.37595","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214987241.pdf","grobid_xml":"https://content.openalex.org/works/W7214987241.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1666907181","https://openalex.org/W2581642134","https://openalex.org/W2150819999","https://openalex.org/W4292721690","https://openalex.org/W2792403630","https://openalex.org/W2962978784","https://openalex.org/W1621867678","https://openalex.org/W7133089259","https://openalex.org/W2783513734","https://openalex.org/W2499149744"],"abstract_inverted_index":{"We":[0],"prove":[1,46],"an":[2,26,31],"analog":[3,50],"of":[4,20,51,58,80,93],"the":[5,9,18,52,87,91,102,107],"Ax-Schanuel":[6,56],"theorem":[7,57,66,79],"for":[8,67],"Drinfeld":[10,108],"$j$-function":[11],"in":[12,41,90,97,106],"odd":[13],"characteristic.":[14],"Roughly":[15],"speaking,":[16],"if":[17],"graph":[19],"$\\boldsymbol{j}\\colon\u03a9^n\\rightarrow\\mathbb{A}^n_{\\mathbb{C}_\\infty}$":[21],"and":[22,62],"its":[23],"derivatives":[24],"has":[25],"atypical":[27],"intersection":[28],"$\\mathcal{V}$":[29,35],"with":[30,101],"algebraic":[32],"variety,":[33],"then":[34],"projects":[36],"to":[37,74,84],"a":[38,47,75],"weakly-special":[39,104],"subvariety":[40],"$\\mathbb{A}^n_{\\mathbb{C}_\\infty}$.":[42],"More":[43],"generally,":[44],"we":[45],"positive":[48],"characteristic":[49],"differential":[53],"Galois":[54],"theoretic":[55],"Bl\u00e1zquez-Sanz,":[59],"Casale,":[60],"Freitag":[61],"Nagloo.":[63],"Our":[64],"main":[65],"$\\boldsymbol{j}$":[68],"follows":[69],"by":[70],"applying":[71],"this":[72,98],"result":[73],"suitable":[76],"foliation.":[77],"A":[78],"Pink":[81],"allows":[82],"us":[83],"conclude":[85],"that":[86],"special":[88],"varieties":[89],"sense":[92],"Bl\u00e1zquez-Sanz":[94],"et":[95],"al.":[96],"context":[99],"agree":[100],"classical":[103],"subvarieties":[105],"sense.":[109]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-01T00:00:00"}
