{"id":"https://openalex.org/W2559613015","doi":null,"title":"Algebraic Stacks with a View Toward Moduli Stacks of Covers","display_name":"Algebraic Stacks with a View Toward Moduli Stacks of Covers","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2559613015","mag":"2559613015"},"language":"en","primary_location":{"id":"mag:2559613015","doi":null,"is_oa":false,"landing_page_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-0348-0487-5_1.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046354438","display_name":"Springer Basel","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Springer Basel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5046354438"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9984999895095825,"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":0.9984999895095825,"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":0.0006000000284984708,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-stacks","display_name":"algebraic stacks","score":0.9980000257492065},{"id":"https://openalex.org/keywords/moduli-stacks","display_name":"moduli stacks","score":0.9129999876022339},{"id":"https://openalex.org/keywords/moduli-space-of-curves","display_name":"moduli space of curves","score":0.7590000033378601},{"id":"https://openalex.org/keywords/algebraic-curves","display_name":"algebraic curves","score":0.5070000290870667},{"id":"https://openalex.org/keywords/deligne-mumford-compactification","display_name":"Deligne-Mumford compactification","score":0.7580000162124634}],"concepts":[{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.8995375633239746},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.8088297247886658},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.7648310661315918},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6688557267189026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.610326886177063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5960005521774292},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.5767924785614014},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.5370302200317383},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5045770406723022},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4643222689628601},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4266957640647888},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4177439212799072},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3779107630252838},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24680587649345398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18698722124099731},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10518607497215271},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2559613015","doi":null,"is_oa":false,"landing_page_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-0348-0487-5_1.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W53621468","https://openalex.org/W119277540","https://openalex.org/W169258215","https://openalex.org/W954650338","https://openalex.org/W1486898453","https://openalex.org/W1495410784","https://openalex.org/W1504189798","https://openalex.org/W1514214675","https://openalex.org/W1520114710","https://openalex.org/W1534976569","https://openalex.org/W1831735236","https://openalex.org/W1970248602","https://openalex.org/W2001793904","https://openalex.org/W2012521620","https://openalex.org/W2014061475","https://openalex.org/W2016963718","https://openalex.org/W2019805641","https://openalex.org/W2037365957","https://openalex.org/W2052579244","https://openalex.org/W2057236959","https://openalex.org/W2058823269","https://openalex.org/W2060140191","https://openalex.org/W2066505712","https://openalex.org/W2066733192","https://openalex.org/W2074129703","https://openalex.org/W2081438487","https://openalex.org/W2102944891","https://openalex.org/W2135327480","https://openalex.org/W2147319630","https://openalex.org/W2151876783","https://openalex.org/W2494683732","https://openalex.org/W2500078391","https://openalex.org/W2578698630","https://openalex.org/W2579365473","https://openalex.org/W2964004969","https://openalex.org/W2964214431"],"related_works":["https://openalex.org/W2989582775","https://openalex.org/W2057236959","https://openalex.org/W7100309227","https://openalex.org/W7099994073","https://openalex.org/W4303195273","https://openalex.org/W7006094310","https://openalex.org/W4309679040","https://openalex.org/W7096831485","https://openalex.org/W7067769450","https://openalex.org/W4390270725"],"abstract_inverted_index":{"Stacks":[0],"arise":[1],"naturally":[2],"in":[3,13,31,94,104,178],"moduli":[4,37,185,202,222],"problems.":[5],"This":[6],"fact":[7],"was":[8],"brilliantly":[9],"foreseen":[10],"by":[11,27],"Mumford":[12,30],"his":[14],"wonderful":[15],"paper":[16],"about":[17,35,92],"Picard":[18],"groups":[19],"of":[20,39,48,57,75,78,109,150,159,165,187,191,204,208,224],"mod-":[21],"uli":[22],"problems":[23],"(47)and":[24],"further":[25],"amplified":[26],"Deligne":[28],"and":[29,155,162],"their":[32],"seminal":[33],"work":[34],"the":[36,45,55,79,89,107,184,201,211],"space":[38],"stable":[40,188],"curves":[41,190,207],"(15).":[42],"Even":[43],"if":[44],"the-":[46],"ory":[47],"stacks":[49,69,93,110,143,216,223],"is":[50,62,86,111],"somewhat":[51],"technical":[52],"due":[53],"to":[54,64,67,87,102,128,172,175],"predominance":[56],"a":[58,71,112,160,198],"functorial":[59],"language,":[60],"it":[61],"important":[63],"be":[65,145],"able":[66],"use":[68,108,176],"without":[70],"complete":[72],"knowl-":[73],"edge":[74],"all":[76],"intricacies":[77],"theory.":[80],"In":[81],"these":[82,105],"notes":[83,166],"our":[84],"aim":[85],"explain":[88],"fundamental":[90],"ideas":[91],"rather":[95],"concrete":[96],"terms.":[97],"As":[98],"we":[99,125],"will":[100],"try":[101],"demonstrate":[103],"notes,":[106],"powerful":[113],"tool":[114],"when":[115,124],"dealing":[116],"with":[117,131,197],"curves,":[118],"or":[119,121],"covers,":[120],"more":[122],"generally":[123],"are":[126],"trying":[127],"classify":[129],"objects":[130,149],"non-trivial":[132],"automorphisms,":[133],"abelian":[134],"varieties,":[135],"vector":[136],"bundles":[137],"etc.":[138],"Many":[139],"people":[140],"think":[141],"that":[142],"should":[144],"considered":[146],"as":[147,219],"basic":[148],"algebraic":[151],"geometry,":[152],"like":[153],"schemes,":[154],"(62)is":[156],"an":[157],"example":[158],"convincing":[161],"heavy":[163],"set":[164],"toward":[167,200],"this":[168],"goal.":[169],"We":[170],"hope":[171],"show":[173],"how":[174],"them":[177],"various":[179],"con-":[180],"crete":[181],"examples,":[182],"especially":[183],"stack":[186,203],"pointed":[189,225],"fixed":[192,209],"genus":[193],"\ufffd\ufffd":[194],"\u2265":[195],"2,":[196],"view":[199],"covers":[205],"between":[206,221],"genera,":[210],"so-called":[212],"Hurwitz":[213,215],"stacks.":[214],"appear":[217],"basically":[218],"correspondences":[220],"curves.":[226],"Mathematics":[227],"Subject":[228],"Classification":[229],"(2010).":[230],"14A20,":[231],"14H10,":[232],"14H30,":[233],"14H37.":[234]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-12-08T00:00:00"}