{"id":"https://openalex.org/W1937430554","doi":"https://doi.org/10.4153/cjm-2015-036-0","title":"On Rational Equivalence in Tropical Geometry","display_name":"On Rational Equivalence in Tropical Geometry","publication_year":2015,"publication_date":"2015-07-17","ids":{"openalex":"https://openalex.org/W1937430554","doi":"https://doi.org/10.4153/cjm-2015-036-0","mag":"1937430554"},"language":"en","primary_location":{"id":"doi:10.4153/cjm-2015-036-0","doi":"https://doi.org/10.4153/cjm-2015-036-0","is_oa":false,"landing_page_url":"https://doi.org/10.4153/cjm-2015-036-0","pdf_url":null,"source":{"id":"https://openalex.org/S131268793","display_name":"Canadian Journal of Mathematics","issn_l":"0008-414X","issn":["0008-414X","1496-4279"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Canadian Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1408.1537","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081594884","display_name":"Lars Allermann","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046","https://openalex.org/I4387152675"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lars Allermann","raw_affiliation_strings":["Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany e-mail:","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082860040","display_name":"Simon Hampe","orcid":"https://orcid.org/0000-0003-4855-120X","observed_orcids":["https://orcid.org/0000-0003-4855-120X"]},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simon Hampe","raw_affiliation_strings":["Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail:","Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail: simon.hampe@"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail:","institution_ids":["https://openalex.org/I91712215"]},{"raw_affiliation_string":"Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail: simon.hampe@","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007518101","display_name":"Johannes Rau","orcid":"https://orcid.org/0000-0002-2392-245X","observed_orcids":["https://orcid.org/0000-0002-2392-245X"]},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Johannes Rau","raw_affiliation_strings":["Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail:","Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail: simon.hampe@"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail:","institution_ids":["https://openalex.org/I91712215"]},{"raw_affiliation_string":"Fachrichtung Mathematik, Universit\u00e4t der Saarlandes, Postfach 151150, 66041 Saarbr\u00fccken, Germany e-mail: simon.hampe@","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":4.3076,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.93683519,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"68","issue":"2","first_page":"241","last_page":"257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9945999979972839,"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":0.9945999979972839,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/rational-equivalence","display_name":"rational equivalence","score":0.8790000081062317},{"id":"https://openalex.org/keywords/tropical-geometry","display_name":"tropical geometry","score":0.8640000224113464},{"id":"https://openalex.org/keywords/tropical-varieties","display_name":"tropical varieties","score":0.8740000128746033},{"id":"https://openalex.org/keywords/chow-groups","display_name":"Chow groups","score":0.7110000252723694},{"id":"https://openalex.org/keywords/hypersurfaces","display_name":"hypersurfaces","score":0.9369999766349792}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8946695327758789},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.736424446105957},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5904160141944885},{"id":"https://openalex.org/C202652594","wikidata":"https://www.wikidata.org/wiki/Q2982669","display_name":"Tropical geometry","level":2,"score":0.585060179233551},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5812726616859436},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5159152746200562},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.506424069404602},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.45726025104522705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43993061780929565},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42031654715538025},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38158857822418213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18264368176460266},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.06817018985748291},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.4153/cjm-2015-036-0","doi":"https://doi.org/10.4153/cjm-2015-036-0","is_oa":false,"landing_page_url":"https://doi.org/10.4153/cjm-2015-036-0","pdf_url":null,"source":{"id":"https://openalex.org/S131268793","display_name":"Canadian Journal of Mathematics","issn_l":"0008-414X","issn":["0008-414X","1496-4279"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Canadian Journal of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1408.1537","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1408.1537","pdf_url":"https://arxiv.org/pdf/1408.1537","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":"pmh:oai:CiteSeerX.psu:10.1.1.569.6791","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.569.6791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.uni-kl.de/~gathmann/pub/14081537.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.757.9840","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.757.9840","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1408.1537.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1408.1537","doi":"https://doi.org/10.48550/arxiv.1408.1537","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1408.1537","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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1408.1537","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1408.1537","pdf_url":"https://arxiv.org/pdf/1408.1537","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/W1937430554.pdf","grobid_xml":"https://content.openalex.org/works/W1937430554.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1481700649","https://openalex.org/W1485445902","https://openalex.org/W1549803340","https://openalex.org/W1609080720","https://openalex.org/W1911454016","https://openalex.org/W1984499246","https://openalex.org/W1997490652","https://openalex.org/W2017840872","https://openalex.org/W2022936939","https://openalex.org/W2036822603","https://openalex.org/W2083387674","https://openalex.org/W2091410157","https://openalex.org/W2142533317","https://openalex.org/W2163903615","https://openalex.org/W2255136811","https://openalex.org/W2533345249","https://openalex.org/W2566917795","https://openalex.org/W2952603636","https://openalex.org/W3102695279","https://openalex.org/W3105737775","https://openalex.org/W3106181011","https://openalex.org/W4256433054"],"related_works":["https://openalex.org/W1549803340","https://openalex.org/W2017840872","https://openalex.org/W2605228556","https://openalex.org/W7204190527","https://openalex.org/W7096160571","https://openalex.org/W2066412388","https://openalex.org/W1911454016","https://openalex.org/W4405956732","https://openalex.org/W4396816846","https://openalex.org/W2979502528"],"abstract_inverted_index":{"Abstract":[0],"This":[1,83],"article":[2],"discusses":[3],"the":[4,20,24,40,53,62,87],"concept":[5],"of":[6,26,44,55,65,79,90],"rational":[7],"equivalence":[8],"in":[9,23,61,74,95],"tropical":[10,27,72,91],"geometry":[11],"(and":[12],"replaces":[13],"an":[14],"older,":[15],"imperfect":[16],"version).":[17],"We":[18,37,68],"give":[19],"basic":[21,35],"definitions":[22],"context":[25],"varieties":[28],"without":[29],"boundary":[30],"points":[31],"and":[32],"prove":[33],"some":[34],"properties.":[36],"then":[38],"compute":[39],"\u201cbounded\u201d":[41],"Chow":[42],"groups":[43],"Rn":[45,75],"by":[46],"showing":[47],"that":[48,70,86],"they":[49],"are":[50],"isomorphic":[51],"to":[52],"group":[54],"fan":[56,81],"cycles.":[57,82],"The":[58],"main":[59],"step":[60],"proof":[63],"is":[64,76,93],"independent":[66],"interest.":[67],"show":[69],"every":[71],"cycle":[73],"a":[77],"sum":[78],"(translated)":[80],"also":[84],"proves":[85],"intersection":[88],"ring":[89],"cycles":[92],"generated":[94],"codimension":[96],"1":[97],"(by":[98],"hypersurfaces).":[99]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
