{"id":"https://openalex.org/W7213500209","doi":"https://doi.org/10.48550/arxiv.2609.18626","title":"On the Stable category of maximal Cohen-Macaulay modules over Gorenstein rings-II","display_name":"On the Stable category of maximal Cohen-Macaulay modules over Gorenstein rings-II","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213500209","doi":"https://doi.org/10.48550/arxiv.2609.18626"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18626","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18626","pdf_url":"https://arxiv.org/pdf/2609.18626","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"},"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/2609.18626","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049108479","display_name":"Tony J. Puthenpurakal","orcid":"https://orcid.org/0000-0002-0559-6355","observed_orcids":["https://orcid.org/0000-0002-0559-6355"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Puthenpurakal, Tony J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5049108479"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9711999893188477,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9711999893188477,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.013399999588727951,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.006899999920278788,"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/stable-categories","display_name":"stable category","score":0.9010000228881836},{"id":"https://openalex.org/keywords/maximal-cohen-macaulay-modules","display_name":"maximal Cohen-Macaulay modules","score":1.0},{"id":"https://openalex.org/keywords/gorenstein-local-rings","display_name":"Gorenstein local rings","score":0.9580000042915344},{"id":"https://openalex.org/keywords/hypersurfaces","display_name":"hypersurfaces","score":0.8209999799728394},{"id":"https://openalex.org/keywords/residue-field","display_name":"residue field","score":0.6499999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8855999708175659},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7339000105857849},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.7077999711036682},{"id":"https://openalex.org/C2781025942","wikidata":"https://www.wikidata.org/wiki/Q7315530","display_name":"Residue field","level":3,"score":0.6442999839782715},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5835999846458435},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5115000009536743},{"id":"https://openalex.org/C118211362","wikidata":"https://www.wikidata.org/wiki/Q1203540","display_name":"Maximal ideal","level":3,"score":0.46480000019073486},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42899999022483826},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3862000107765198},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37290000915527344},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C11846945","wikidata":"https://www.wikidata.org/wiki/Q1082992","display_name":"Equivalence of categories","level":3,"score":0.33570000529289246},{"id":"https://openalex.org/C2780212368","wikidata":"https://www.wikidata.org/wiki/Q7840150","display_name":"Triangulated category","level":4,"score":0.33399999141693115}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18626","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18626","pdf_url":"https://arxiv.org/pdf/2609.18626","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":"doi:10.48550/arxiv.2609.18626","doi":"https://doi.org/10.48550/arxiv.2609.18626","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18626","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:2609.18626","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18626","pdf_url":"https://arxiv.org/pdf/2609.18626","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/W7213500209.pdf","grobid_xml":"https://content.openalex.org/works/W7213500209.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3181534484","https://openalex.org/W4411655833","https://openalex.org/W4406151049","https://openalex.org/W4233356238","https://openalex.org/W6983525970","https://openalex.org/W3080344081","https://openalex.org/W1973888818","https://openalex.org/W7101194684","https://openalex.org/W4415275338","https://openalex.org/W2963295766"],"abstract_inverted_index":{"Let":[0],"$(A,\\mathfrak{m}),":[1],"(B,\\mathfrak{n})":[2],"$":[3],"be":[4,11],"Gorenstein":[5,146],"local":[6],"rings":[7],"and":[8,73,92,125],"let":[9],"$\\underline{CM}(A)$":[10],"its":[12],"stable":[13,161],"category":[14,162],"of":[15,89,104,113,116,120,123,163,183],"finitely":[16],"generated":[17],"maximal":[18,52,166],"Cohen-Macaulay":[19,167],"$A$-modules.":[20],"Suppose":[21],"we":[22,148],"have":[23],"an":[24,131,174],"equivalence":[25,175],"$\u03a6\\colon\\underline{CM}(A)":[26],"\\rightarrow":[27,155],"\\underline{CM}(A)$":[28,156],"as":[29],"triangulated":[30,151],"categories.":[31],"We":[32,106,169,179],"show":[33,108,170],"(1)":[34],"If":[35,48],"$A,":[36],"B$":[37],"are":[38],"not":[39],"hypersurfaces":[40],"then":[41,56,147],"$dim":[42],"A":[43],"=":[44,58,63,142],"dim":[45],"B$.":[46],"(2)":[47],"$M$":[49],"is":[50,81,96,130,145,159],"a":[51,82,97,150],"\\CM":[53],"\\":[54],"$A$-module":[55],"$$\\text{curv}_A(M)":[57],"\\text{curv}_B":[59],"(\u03a6(M)),$$":[60],"here":[61],"$\\text{curv}_A(M)":[62],"\\limsup_n":[64],"\\sqrt[n]{\\ell(\\text{Tor}^A_n(M,k))}$.":[65],"(3)":[66],"$A$":[67,80,90,124,134],"satisfies":[68,77],"Serre's":[69],"condition":[70],"$R_i$":[71],"if":[72,75,91,94,128],"only":[74,93],"$B$":[76,95,117],"$R_i$.":[78],"(4)":[79],"complete":[83,98],"intersection":[84,99],"on":[85,100],"the":[86,101,137,160],"punctured":[87,102],"spectrum":[88,103],"$B$.":[105],"also":[107],"that":[109,136,171],"$\u03a6$":[110],"imposes":[111],"constraints":[112],"residue":[114,121],"field":[115,122],"in":[118,133],"terms":[119],"vice-versa.":[126],"Finally":[127],"$I$":[129],"ideal":[132],"such":[135],"extended":[138],"Rees":[139],"algebra":[140],"$\\mathcal{R}(I)":[141],"A[It,":[143],"t^{-1}]$":[144],"construct":[149],"functor":[152],"$\u03a8\\colon":[153],"\\underline{CM}^\\mathbb{Z}(\\mathcal{R}(I))":[154],"where":[157],"$\\underline{CM}^\\mathbb{Z}(\\mathcal{R}(I))$":[158],"all":[164],"graded":[165],"$\\mathcal{R}(I)$-modules.":[168],"$\u03a8$":[172],"induces":[173],"$\\underline{CM}^\\mathbb{Z}(\\mathcal{R}(I))/\\ker":[176],"\u03a8\\rightarrow":[177],"\\underline{CM}(A)$.":[178],"give":[180],"some":[181],"applications":[182],"this":[184],"map.":[185]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-18T00:00:00"}