{"id":"https://openalex.org/W7207880368","doi":"https://doi.org/10.48550/arxiv.2609.01298","title":"Fourier--Mukai loci are open and base change","display_name":"Fourier--Mukai loci are open and base change","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7207880368","doi":"https://doi.org/10.48550/arxiv.2609.01298"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01298","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01298","pdf_url":"https://arxiv.org/pdf/2609.01298","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5149758026","display_name":"El\u00edas Guisado Villalgordo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Villalgordo, El\u00edas Guisado","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043539850","display_name":"Pat Lank","orcid":"https://orcid.org/0000-0002-2367-2892","observed_orcids":["https://orcid.org/0000-0002-2367-2892"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lank, Pat","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":3,"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":0.9810000061988831,"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":0.9810000061988831,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.013000000268220901,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0012000000569969416,"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/fourier-mukai-transform","display_name":"Fourier-Mukai transform","score":0.9369999766349792},{"id":"https://openalex.org/keywords/algebraic-spaces","display_name":"algebraic spaces","score":0.8109999895095825},{"id":"https://openalex.org/keywords/base-change","display_name":"base change","score":0.8730000257492065},{"id":"https://openalex.org/keywords/elliptic-fibrations","display_name":"elliptic fibrations","score":0.9990000128746033}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6383000016212463},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6205999851226807},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5196999907493591},{"id":"https://openalex.org/C84976871","wikidata":"https://www.wikidata.org/wiki/Q2015673","display_name":"Openness to experience","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44600000977516174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3571000099182129},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.2994000017642975},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01298","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01298","pdf_url":"https://arxiv.org/pdf/2609.01298","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.2609.01298","doi":"https://doi.org/10.48550/arxiv.2609.01298","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01298","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:2609.01298","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01298","pdf_url":"https://arxiv.org/pdf/2609.01298","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/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207880368.pdf","grobid_xml":"https://content.openalex.org/works/W7207880368.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1563009405","https://openalex.org/W4391672947","https://openalex.org/W4403852134","https://openalex.org/W4406797125","https://openalex.org/W4410348594","https://openalex.org/W4417530315","https://openalex.org/W7119478259"],"related_works":["https://openalex.org/W4417530315","https://openalex.org/W7099579599","https://openalex.org/W2150706552","https://openalex.org/W7096064675","https://openalex.org/W7134045722","https://openalex.org/W7223222353","https://openalex.org/W7160241589","https://openalex.org/W2952357425","https://openalex.org/W2181359795","https://openalex.org/W2075238885"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,17],"theory":[3],"of":[4],"relative":[5],"(quasi-)perfect":[6],"complexes":[7],"for":[8,16,60],"algebraic":[9],"spaces.":[10],"Our":[11],"main":[12],"result":[13],"proves":[14],"that":[15,65],"pseudocoherent":[18],"kernel":[19,41],"relatively":[20],"perfect":[21],"over":[22],"both":[23],"factors,":[24],"the":[25],"loci":[26,48],"where":[27],"its":[28],"fiberwise":[29],"Fourier--Mukai":[30],"transform":[31],"is":[32],"fully":[33],"faithful":[34],"or":[35],"an":[36,57],"equivalence":[37],"are":[38,69],"open.":[39],"The":[40],"need":[42],"not":[43],"be":[44],"perfect,":[45],"and":[46,63,67],"these":[47],"commute":[49],"with":[50],"Noetherian":[51],"base":[52],"change.":[53],"Moreover,":[54],"we":[55],"provide":[56],"explicit":[58],"autoequivalence":[59],"elliptic":[61],"fibrations,":[62],"establish":[64],"smoothness":[66],"Gorensteinness":[68],"derived":[70],"invariants.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-04T00:00:00"}