K-theory of cones of smooth varieties

Autores
Cortiñas, Guillermo Horacio; Haesemeyer, Christian; Walker, Mark E.; Weibel, Charles A.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H1 (C, O(n)). The formula for K0(R) involves the Zariski cohomology of twisted K¨ahler differentials on the variety.
Fil: Cortiñas, Guillermo Horacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina
Fil: Haesemeyer, Christian. University of California at Los Angeles; Estados Unidos
Fil: Walker, Mark E.. Universidad de Nebraska - Lincoln; Estados Unidos
Fil: Weibel, Charles A.. Rutgers University; Estados Unidos
Materia
Algebraic K-theory
Affine cone
Cohomology of differential forms
Cyclic homology
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14841
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14841
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling K-theory of cones of smooth varietiesCortiñas, Guillermo HoracioHaesemeyer, ChristianWalker, Mark E.Weibel, Charles A.Algebraic K-theoryAffine coneCohomology of differential formsCyclic homologyhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H1 (C, O(n)). The formula for K0(R) involves the Zariski cohomology of twisted K¨ahler differentials on the variety.Fil: Cortiñas, Guillermo Horacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; ArgentinaFil: Haesemeyer, Christian. University of California at Los Angeles; Estados UnidosFil: Walker, Mark E.. Universidad de Nebraska - Lincoln; Estados UnidosFil: Weibel, Charles A.. Rutgers University; Estados UnidosUniv Press Inc2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14841Cortiñas, Guillermo Horacio; Haesemeyer, Christian; Walker, Mark E.; Weibel, Charles A.; K-theory of cones of smooth varieties; Univ Press Inc; Journal Of Algebraic Geometry; 22; 1; 2-2013; 13-341056-3911enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/jag/2013-22-01/S1056-3911-2011-00583-3/info:eu-repo/semantics/altIdentifier/doi/10.1090/S1056-3911-2011-00583-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:41:30Zoai:ri.conicet.gov.ar:11336/14841instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 10:41:30.521CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv K-theory of cones of smooth varieties
title K-theory of cones of smooth varieties
spellingShingle K-theory of cones of smooth varieties
Cortiñas, Guillermo Horacio
Algebraic K-theory
Affine cone
Cohomology of differential forms
Cyclic homology
title_short K-theory of cones of smooth varieties
title_full K-theory of cones of smooth varieties
title_fullStr K-theory of cones of smooth varieties
title_full_unstemmed K-theory of cones of smooth varieties
title_sort K-theory of cones of smooth varieties
dc.creator.none.fl_str_mv Cortiñas, Guillermo Horacio
Haesemeyer, Christian
Walker, Mark E.
Weibel, Charles A.
author Cortiñas, Guillermo Horacio
author_facet Cortiñas, Guillermo Horacio
Haesemeyer, Christian
Walker, Mark E.
Weibel, Charles A.
author_role author
author2 Haesemeyer, Christian
Walker, Mark E.
Weibel, Charles A.
author2_role author
author
author
dc.subject.none.fl_str_mv Algebraic K-theory
Affine cone
Cohomology of differential forms
Cyclic homology
topic Algebraic K-theory
Affine cone
Cohomology of differential forms
Cyclic homology
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H1 (C, O(n)). The formula for K0(R) involves the Zariski cohomology of twisted K¨ahler differentials on the variety.
Fil: Cortiñas, Guillermo Horacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina
Fil: Haesemeyer, Christian. University of California at Los Angeles; Estados Unidos
Fil: Walker, Mark E.. Universidad de Nebraska - Lincoln; Estados Unidos
Fil: Weibel, Charles A.. Rutgers University; Estados Unidos
description Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H1 (C, O(n)). The formula for K0(R) involves the Zariski cohomology of twisted K¨ahler differentials on the variety.
publishDate 2013
dc.date.none.fl_str_mv 2013-02
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/11336/14841
Cortiñas, Guillermo Horacio; Haesemeyer, Christian; Walker, Mark E.; Weibel, Charles A.; K-theory of cones of smooth varieties; Univ Press Inc; Journal Of Algebraic Geometry; 22; 1; 2-2013; 13-34
1056-3911
url http://hdl.handle.net/11336/14841
identifier_str_mv Cortiñas, Guillermo Horacio; Haesemeyer, Christian; Walker, Mark E.; Weibel, Charles A.; K-theory of cones of smooth varieties; Univ Press Inc; Journal Of Algebraic Geometry; 22; 1; 2-2013; 13-34
1056-3911
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/jag/2013-22-01/S1056-3911-2011-00583-3/
info:eu-repo/semantics/altIdentifier/doi/10.1090/S1056-3911-2011-00583-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Univ Press Inc
publisher.none.fl_str_mv Univ Press Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1847978111364235264
score 13.087074

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