{"id":"https://openalex.org/W2554747494","doi":"https://doi.org/10.14736/kyb-2022-5-0790","title":"The universal tropicalization and the Berkovich analytification","display_name":"The universal tropicalization and the Berkovich analytification","publication_year":2023,"publication_date":"2023-01-19","ids":{"openalex":"https://openalex.org/W2554747494","doi":"https://doi.org/10.14736/kyb-2022-5-0790","mag":"2554747494"},"language":"en","primary_location":{"id":"doi:10.14736/kyb-2022-5-0790","is_oa":true,"landing_page_url":"http://dx.doi.org/10.14736/kyb-2022-5-0790","pdf_url":"https://www.kybernetika.cz/content/2022/5/790/paper.pdf","source":{"id":"https://openalex.org/S158577884","display_name":"Kybernetika","issn_l":"0023-5954","issn":["0023-5954","1805-949X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310314340","host_organization_name":"Institute of Information Theory and Automation of the Czech Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310314340","https://openalex.org/P4310314171"],"host_organization_lineage_names":["Institute of Information Theory and Automation of the Czech Academy of Sciences","Czech Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kybernetika","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.kybernetika.cz/content/2022/5/790/paper.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057669183","display_name":"Jeffrey Giansiracusa","orcid":"https://orcid.org/0000-0003-4252-0058"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jeffrey Giansiracusa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033650471","display_name":"Noah Giansiracusa","orcid":"https://orcid.org/0000-0001-7903-5836"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Noah Giansiracusa","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057669183"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7899,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.73597557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"790","last_page":"815"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9990000128746033,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.998199999332428,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7005298137664795},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6824243068695068},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6535746455192566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5827727913856506},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.49563467502593994},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.49554455280303955},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4172821640968323},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3403993248939514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12760749459266663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10738638043403625}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7005298137664795},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6824243068695068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6535746455192566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5827727913856506},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.49563467502593994},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.49554455280303955},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4172821640968323},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3403993248939514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12760749459266663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10738638043403625},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.14736/kyb-2022-5-0790","is_oa":true,"landing_page_url":"http://dx.doi.org/10.14736/kyb-2022-5-0790","pdf_url":"https://www.kybernetika.cz/content/2022/5/790/paper.pdf","source":{"id":"https://openalex.org/S158577884","display_name":"Kybernetika","issn_l":"0023-5954","issn":["0023-5954","1805-949X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310314340","host_organization_name":"Institute of Information Theory and Automation of the Czech Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310314340","https://openalex.org/P4310314171"],"host_organization_lineage_names":["Institute of Information Theory and Automation of the Czech Academy of Sciences","Czech Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kybernetika","raw_type":"journal-article"},{"id":"pmh:oai:dro.dur.ac.uk.OAI2:36719","is_oa":false,"landing_page_url":"http://dro.dur.ac.uk/36719/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196258","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Kybernetika, 2022, Vol.58(5), pp.790-815 [Peer Reviewed Journal]","raw_type":"Article"},{"id":"pmh:oai:oai.dml.cz:10338.dmlcz/151304","is_oa":true,"landing_page_url":"http://hdl.handle.net/10338.dmlcz/151304","pdf_url":"http://dml.cz/bitstream/handle/10338.dmlcz/151304/Kybernetika_58-2022-5_9.pdf","source":{"id":"https://openalex.org/S4406922294","display_name":"Czech digital mathematics library","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text:not_categorized"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.742.6818","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.742.6818","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/1410.4348.pdf","raw_type":"text"},{"id":"pmh:oai:durham-repository.worktribe.com:1194769","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1194769","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"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":"publishedVersion"}],"best_oa_location":{"id":"doi:10.14736/kyb-2022-5-0790","is_oa":true,"landing_page_url":"http://dx.doi.org/10.14736/kyb-2022-5-0790","pdf_url":"https://www.kybernetika.cz/content/2022/5/790/paper.pdf","source":{"id":"https://openalex.org/S158577884","display_name":"Kybernetika","issn_l":"0023-5954","issn":["0023-5954","1805-949X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310314340","host_organization_name":"Institute of Information Theory and Automation of the Czech Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310314340","https://openalex.org/P4310314171"],"host_organization_lineage_names":["Institute of Information Theory and Automation of the Czech Academy of Sciences","Czech Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kybernetika","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6800000071525574,"display_name":"Life below water","id":"https://metadata.un.org/sdg/14"}],"awards":[{"id":"https://openalex.org/G3330119427","display_name":null,"funder_award_id":"EPSRC","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3498186453","display_name":"PostDoctoral Research Fellowship","funder_award_id":"1204440","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7242211680","display_name":"Moduli spaces from a topological point of view","funder_award_id":"EP/I003908/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2554747494.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W310036830","https://openalex.org/W1489661707","https://openalex.org/W1490953708","https://openalex.org/W1507909509","https://openalex.org/W1549562143","https://openalex.org/W1550400925","https://openalex.org/W1579203665","https://openalex.org/W1609080720","https://openalex.org/W1690238531","https://openalex.org/W1838788336","https://openalex.org/W1990775160","https://openalex.org/W2025863922","https://openalex.org/W2074740609","https://openalex.org/W2131440188","https://openalex.org/W2154785235","https://openalex.org/W2157796248","https://openalex.org/W2486839744","https://openalex.org/W2593283098","https://openalex.org/W2952603636","https://openalex.org/W2962910040","https://openalex.org/W2963114720","https://openalex.org/W2963147012","https://openalex.org/W2963674602","https://openalex.org/W2963821233","https://openalex.org/W2963912243","https://openalex.org/W2990393058","https://openalex.org/W3037615322","https://openalex.org/W3038041243","https://openalex.org/W3083386533","https://openalex.org/W3099375060","https://openalex.org/W3099409833","https://openalex.org/W3122258138","https://openalex.org/W4205387864","https://openalex.org/W4242642882","https://openalex.org/W4244178334","https://openalex.org/W4287083538","https://openalex.org/W4293097209","https://openalex.org/W4298023459","https://openalex.org/W4301487749","https://openalex.org/W4302277276","https://openalex.org/W6606581339"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W2183306018","https://openalex.org/W2549990292","https://openalex.org/W2345479200","https://openalex.org/W2239445980"],"abstract_inverted_index":{"ABSTRACT.":[0],"Given":[1],"an":[2,44],"integral":[3],"scheme":[4,85],"X":[5,19,51,62,117,134,169],"over":[6,27],"a":[7,14,21,25,37,48,83,145,149,177],"non-archimedean":[8],"valued":[9],"field":[10,29],"k,":[11],"we":[12,55,81,123,155],"construct":[13],"universal":[15,67,114,178,192],"closed":[16],"embedding":[17,41,68],"of":[18,36,50,61,79,101,130,133,148,152,163,187],"into":[20,42],"k-scheme":[22],"equipped":[23],"with":[24,30,63,135],"model":[26],"the":[28,58,70,76,90,106,109,113,128,131,160,185,191],"one":[31],"element":[32],"F1":[33],"(a":[34],"generalization":[35],"toric":[38],"variety).":[39],"An":[40],"such":[43],"ambient":[45],"space":[46],"determines":[47],"tropicalization":[49,60,78],"by":[52],"[GG13],":[53,80],"and":[54,92,167],"show":[56,124,156],"that":[57,93,108,125,157],"set-theoretic":[59],"respect":[64,136],"to":[65,96,137],"this":[66],"is":[69,112,121,127,173,176],"Berkovich":[71,110],"analytification":[72,91,111],"Xan.":[73],"Moreover,":[74],"using":[75],"scheme-theoretic":[77,99,146],"obtain":[82],"tropical":[84],"Tropuniv(X)":[86,126,158],"whose":[87],"T-points":[88],"give":[89],"canonically":[94],"maps":[95],"all":[97,138],"other":[98],"tropicalizations":[100,132],"X.":[102],"This":[103],"makes":[104],"precise":[105],"idea":[107],"tropicalization.":[115,193],"When":[116],"=":[118,170],"Spec":[119,171],"A":[120,172,181],"affine,":[122],"limit":[129],"embeddings":[139],"in":[140,184],"affine":[141,174],"space,":[142],"thus":[143],"giving":[144],"enrichment":[147],"well-known":[150],"result":[151],"Payne.":[153],"Finally,":[154],"represents":[159],"moduli":[161],"functor":[162],"valuations":[164],"on":[165,180,190],"X,":[166],"when":[168],"there":[175],"valuation":[179],"taking":[182],"values":[183],"semiring":[186],"regular":[188],"functions":[189],"1.":[194]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
