{"id":"https://openalex.org/W4383175645","doi":"https://doi.org/10.4230/lipics.types.2024.3","title":"A Foundation for Synthetic Algebraic Geometry","display_name":"A Foundation for Synthetic Algebraic Geometry","publication_year":2023,"publication_date":"2023-06-30","ids":{"openalex":"https://openalex.org/W4383175645","doi":"https://doi.org/10.4230/lipics.types.2024.3"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2307.00073","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.00073","pdf_url":"https://arxiv.org/pdf/2307.00073","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2307.00073","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008848883","display_name":"Felix Cherubini","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Cherubini, Felix","raw_affiliation_strings":["University of Gothenburg, Sweden","Chalmers University of Technology, Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"University of Gothenburg, Sweden","institution_ids":["https://openalex.org/I881427289"]},{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087100539","display_name":"Thierry Coquand","orcid":"https://orcid.org/0000-0002-5429-5153"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Coquand, Thierry","raw_affiliation_strings":["University of Gothenburg, Sweden","Chalmers University of Technology, Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"University of Gothenburg, Sweden","institution_ids":["https://openalex.org/I881427289"]},{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Geerligs, Freek","orcid":"https://orcid.org/0009-0003-6938-4807"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Geerligs, Freek","raw_affiliation_strings":["University of Gothenburg, Sweden","Chalmers University of Technology, Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"University of Gothenburg, Sweden","institution_ids":["https://openalex.org/I881427289"]},{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":null,"display_name":"Moeneclaey, Hugo","orcid":"https://orcid.org/0000-0002-8579-0077"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Moeneclaey, Hugo","raw_affiliation_strings":["University of Gothenburg, Sweden","Chalmers University of Technology, Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"University of Gothenburg, Sweden","institution_ids":["https://openalex.org/I881427289"]},{"raw_affiliation_string":"Chalmers University of Technology, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5008848883"],"corresponding_institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16584464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9980000257492065,"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/T12069","display_name":"Commutative Algebra and Its Applications","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/T11752","display_name":"Cancer Treatment and Pharmacology","score":0.9616000056266785,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7893353700637817},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.7604316473007202},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7283967733383179},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.6935054063796997},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.601209282875061},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4622392952442169},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.45563167333602905},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.449873149394989},{"id":"https://openalex.org/keywords/motivic-cohomology","display_name":"Motivic cohomology","score":0.4261886477470398},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.4210784435272217},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.42085781693458557},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.4151977598667145},{"id":"https://openalex.org/keywords/foundation","display_name":"Foundation (evidence)","score":0.41324636340141296},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.37551772594451904},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26918694376945496},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.133175790309906},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1296379566192627},{"id":"https://openalex.org/keywords/equivariant-cohomology","display_name":"Equivariant cohomology","score":0.11912333965301514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1116955578327179},{"id":"https://openalex.org/keywords/de-rham-cohomology","display_name":"De Rham cohomology","score":0.09533378481864929},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.0753985345363617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7893353700637817},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.7604316473007202},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7283967733383179},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6935054063796997},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.601209282875061},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4622392952442169},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.45563167333602905},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.449873149394989},{"id":"https://openalex.org/C84254916","wikidata":"https://www.wikidata.org/wiki/Q2981889","display_name":"Motivic cohomology","level":5,"score":0.4261886477470398},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4210784435272217},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.42085781693458557},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.4151977598667145},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.41324636340141296},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.37551772594451904},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26918694376945496},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.133175790309906},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1296379566192627},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.11912333965301514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1116955578327179},{"id":"https://openalex.org/C68365058","wikidata":"https://www.wikidata.org/wiki/Q1179446","display_name":"De Rham cohomology","level":4,"score":0.09533378481864929},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0753985345363617},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2307.00073","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.00073","pdf_url":"https://arxiv.org/pdf/2307.00073","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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.2307.00073","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2307.00073","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.4230/lipics.types.2024.3","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.types.2024.3","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2307.00073","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.00073","pdf_url":"https://arxiv.org/pdf/2307.00073","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383175645.pdf","grobid_xml":"https://content.openalex.org/works/W4383175645.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3110986101","https://openalex.org/W4246327958","https://openalex.org/W2579704584","https://openalex.org/W4319982912","https://openalex.org/W2803072931","https://openalex.org/W376795554","https://openalex.org/W3004463896","https://openalex.org/W302516208","https://openalex.org/W1979204163","https://openalex.org/W2884963758"],"abstract_inverted_index":{"The":[0],"language":[1,13],"of":[2,39,43,62,82,89,109,150,204],"homotopy":[3,67,153],"type":[4,68,88,97,154],"theory":[5,69],"has":[6],"proved":[7],"to":[8,31,51,137,181],"be":[9,52,173],"an":[10,53,197],"appropriate":[11,54],"internal":[12],"for":[14,18,20,35,56,162,168],"various":[15],"higher":[16,37],"toposes,":[17],"example":[19],"the":[21,33,36,60,80,133,142,147,193],"Zariski":[22],"topos":[23,38],"in":[24,59,141,152],"Synthetic":[25],"Algebraic":[26],"Geometry.":[27],"This":[28,49,126],"paper":[29],"aims":[30],"do":[32],"same":[34],"light":[40],"condensed":[41],"anima":[42],"Dustin":[44],"Clausen":[45],"and":[46,79,113,117,165,186],"Peter":[47],"Scholze.":[48],"seems":[50],"setting":[55],"synthetic":[57,107,202],"topology":[58,94],"style":[61],"Mart\u00edn":[63],"Escard\u00f3.":[64],"We":[65,74,104,178],"use":[66,179],"extended":[70],"with":[71],"4":[72],"axioms.":[73],"prove":[75,182],"Markov\u2019s":[76],"principle,":[77],"LLPO":[78],"negation":[81],"WLPO.":[83],"Then":[84],"we":[85,156,199],"define":[86],"a":[87,93,106,201],"open":[90],"propositions,":[91],"inducing":[92],"on":[95],"any":[96,100,129],"such":[98],"that":[99,119,128,158,166],"map":[101,130],"is":[102,139,192],"continuous.":[103],"give":[105,200],"definition":[108,149],"second":[110],"countable":[111],"Stone":[112,164],"compact":[114,170],"Hausdorff":[115,171],"spaces,":[116],"show":[118,157],"their":[120],"induced":[121],"topologies":[122],"are":[123],"as":[124],"expected.":[125],"means":[127],"from":[131],"e.g.":[132],"unit":[134],"interval":[135],"\ud835\udd40":[136],"itself":[138],"continuous":[140],"usual":[143,148],"epsilon-delta":[144],"sense.":[145],"With":[146],"cohomology":[151],"theory,":[155],"H\u00b9(S,\u2124)":[159],"=":[160,184,188],"0":[161,185],"S":[163],"H\u00b9(X,\u2124)":[167],"X":[169],"can":[172],"computed":[174],"using":[175],"\u010cech":[176],"cohomology.":[177],"this":[180],"H\u00b9(\ud835\udd40\u00b9,\u2124)":[183],"H\u00b9(\ud835\udd4a\u00b9,\u2124)":[187],"\u2124":[189],"where":[190],"\ud835\udd4a\u00b9":[191],"set":[194],"\u211d/\u2124.":[195],"As":[196],"application,":[198],"proof":[203],"Brouwer\u2019s":[205],"fixed-point":[206],"theorem.":[207]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2023-07-05T00:00:00"}