De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry

Autores
Cortiñas, G.
Año de publicación
2003
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The title refers to the nilcommutative of NC-schemes introduced by M. Kapranov in 'Noncommutative Geometry Based on Commutator Expansions', J. Reine Angew. Math 505 (1998) 73-118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson of NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306-358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.
Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Compos. Math. 2003;136(2):171-208
Materia
Commutator filtration
Cyclic homology
Grothendieck topology
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0010437X_v136_n2_p171_Cortinas
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repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic GeometryCortiñas, G.Commutator filtrationCyclic homologyGrothendieck topologyThe title refers to the nilcommutative of NC-schemes introduced by M. Kapranov in 'Noncommutative Geometry Based on Commutator Expansions', J. Reine Angew. Math 505 (1998) 73-118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson of NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306-358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2003info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0010437X_v136_n2_p171_CortinasCompos. Math. 2003;136(2):171-208reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2026-09-24T11:34:40Zpaperaa:paper_0010437X_v136_n2_p171_CortinasInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962026-09-24 11:34:43.575Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
title De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
spellingShingle De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
Cortiñas, G.
Commutator filtration
Cyclic homology
Grothendieck topology
title_short De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
title_full De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
title_fullStr De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
title_full_unstemmed De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
title_sort De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry
dc.creator.none.fl_str_mv Cortiñas, G.
author Cortiñas, G.
author_facet Cortiñas, G.
author_role author
dc.subject.none.fl_str_mv Commutator filtration
Cyclic homology
Grothendieck topology
topic Commutator filtration
Cyclic homology
Grothendieck topology
dc.description.none.fl_txt_mv The title refers to the nilcommutative of NC-schemes introduced by M. Kapranov in 'Noncommutative Geometry Based on Commutator Expansions', J. Reine Angew. Math 505 (1998) 73-118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson of NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306-358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.
Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description The title refers to the nilcommutative of NC-schemes introduced by M. Kapranov in 'Noncommutative Geometry Based on Commutator Expansions', J. Reine Angew. Math 505 (1998) 73-118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson of NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306-358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.
publishDate 2003
dc.date.none.fl_str_mv 2003
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_0010437X_v136_n2_p171_Cortinas
url http://hdl.handle.net/20.500.12110/paper_0010437X_v136_n2_p171_Cortinas
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Compos. Math. 2003;136(2):171-208
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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