The Hilbert-Kunz function of some quadratic quotients of the Rees algebra

Given a commutative local ring $(R, \mathfrak{m})$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[I t]$ has been recently studied as a unified approach to the Nagata's idealization and the amalgamated duplication and as a way to construct interesting examples, especially...

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Autores: Strazzanti, Francesco, Zarzuela, Santiago
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/193549
Acceso en línea:https://hdl.handle.net/2445/193549
Access Level:acceso abierto
Palabra clave:Anells locals
Àlgebra commutativa
Àlgebra homològica
Local rings
Commutative algebra
Homological algebra
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spelling The Hilbert-Kunz function of some quadratic quotients of the Rees algebraStrazzanti, FrancescoZarzuela, SantiagoAnells localsÀlgebra commutativaÀlgebra homològicaLocal ringsCommutative algebraHomological algebraGiven a commutative local ring $(R, \mathfrak{m})$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[I t]$ has been recently studied as a unified approach to the Nagata's idealization and the amalgamated duplication and as a way to construct interesting examples, especially integral domains. When $R$ is noetherian of prime characteristic, we compute the HilbertKunz function of the members of this family and, provided that either $I$ is $\mathfrak{m}$-primary or $R$ is regular and F-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored.American Mathematical Society (AMS)2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/193549Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1090/proc/15819Proceedings of the American Mathematical Society, 2022, vol. 150, num. 4, p. 1493-1503https://doi.org/10.1090/proc/15819cc-by-nc-nd (c) American Mathematical Society (AMS), 2022https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1935492026-05-27T06:46:51Z
dc.title.none.fl_str_mv The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
title The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
spellingShingle The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
Strazzanti, Francesco
Anells locals
Àlgebra commutativa
Àlgebra homològica
Local rings
Commutative algebra
Homological algebra
title_short The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
title_full The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
title_fullStr The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
title_full_unstemmed The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
title_sort The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
dc.creator.none.fl_str_mv Strazzanti, Francesco
Zarzuela, Santiago
author Strazzanti, Francesco
author_facet Strazzanti, Francesco
Zarzuela, Santiago
author_role author
author2 Zarzuela, Santiago
author2_role author
dc.subject.none.fl_str_mv Anells locals
Àlgebra commutativa
Àlgebra homològica
Local rings
Commutative algebra
Homological algebra
topic Anells locals
Àlgebra commutativa
Àlgebra homològica
Local rings
Commutative algebra
Homological algebra
description Given a commutative local ring $(R, \mathfrak{m})$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[I t]$ has been recently studied as a unified approach to the Nagata's idealization and the amalgamated duplication and as a way to construct interesting examples, especially integral domains. When $R$ is noetherian of prime characteristic, we compute the HilbertKunz function of the members of this family and, provided that either $I$ is $\mathfrak{m}$-primary or $R$ is regular and F-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/193549
url https://hdl.handle.net/2445/193549
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1090/proc/15819
Proceedings of the American Mathematical Society, 2022, vol. 150, num. 4, p. 1493-1503
https://doi.org/10.1090/proc/15819
dc.rights.none.fl_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2022
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2022
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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