On the Derived Invariance of Cohomology Theories for Coalgebras

We study the derived invariance of the cohomology theories Hoch*, H* and HC* associated with coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: (1) f: C → D a quasi-isomorphism of differential graded coalge...

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Autor principal: Farinati, Marco Andres
Publicado: 2003
Materias:
Coalgebras
Derived categories
Hochschild homology
Geometry
Problem solving
Theorem proving
Algebra
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v6_n3_p303_Farinati
http://hdl.handle.net/20.500.12110/paper_1386923X_v6_n3_p303_Farinati
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_1386923X_v6_n3_p303_Farinati
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spelling paper:paper_1386923X_v6_n3_p303_Farinati2023-06-08T16:12:52Z On the Derived Invariance of Cohomology Theories for Coalgebras Farinati, Marco Andres Coalgebras Derived categories Hochschild homology Geometry Problem solving Theorem proving Derived categories Algebra We study the derived invariance of the cohomology theories Hoch*, H* and HC* associated with coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: (1) f: C → D a quasi-isomorphism of differential graded coalgebras, (2) the existence of a 'cotilting' bicomodule CTD In these two cases we construct a derived-Morita equivalence context, and consequently we obtain isomorphisms Hoch*(C) ≅ Hoch*(D) and H*(C) ≅ H*(D). Moreover, when we have a coassociative map inducing an isomorphism H*(C) ≅ H* (D) (for example, when there is a quasi-isomorphism f: C → D), we prove that HC*(C) ≅ HC*(D). Fil:Farinati, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v6_n3_p303_Farinati http://hdl.handle.net/20.500.12110/paper_1386923X_v6_n3_p303_Farinati
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Coalgebras
Derived categories
Hochschild homology
Geometry
Problem solving
Theorem proving
Derived categories
Algebra
spellingShingle Coalgebras
Derived categories
Hochschild homology
Geometry
Problem solving
Theorem proving
Derived categories
Algebra
Farinati, Marco Andres
On the Derived Invariance of Cohomology Theories for Coalgebras
topic_facet Coalgebras
Derived categories
Hochschild homology
Geometry
Problem solving
Theorem proving
Derived categories
Algebra
description We study the derived invariance of the cohomology theories Hoch*, H* and HC* associated with coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: (1) f: C → D a quasi-isomorphism of differential graded coalgebras, (2) the existence of a 'cotilting' bicomodule CTD In these two cases we construct a derived-Morita equivalence context, and consequently we obtain isomorphisms Hoch*(C) ≅ Hoch*(D) and H*(C) ≅ H*(D). Moreover, when we have a coassociative map inducing an isomorphism H*(C) ≅ H* (D) (for example, when there is a quasi-isomorphism f: C → D), we prove that HC*(C) ≅ HC*(D).
author Farinati, Marco Andres
author_facet Farinati, Marco Andres
author_sort Farinati, Marco Andres
title On the Derived Invariance of Cohomology Theories for Coalgebras
title_short On the Derived Invariance of Cohomology Theories for Coalgebras
title_full On the Derived Invariance of Cohomology Theories for Coalgebras
title_fullStr On the Derived Invariance of Cohomology Theories for Coalgebras
title_full_unstemmed On the Derived Invariance of Cohomology Theories for Coalgebras
title_sort on the derived invariance of cohomology theories for coalgebras
publishDate 2003
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v6_n3_p303_Farinati
http://hdl.handle.net/20.500.12110/paper_1386923X_v6_n3_p303_Farinati
work_keys_str_mv AT farinatimarcoandres onthederivedinvarianceofcohomologytheoriesforcoalgebras
_version_ 1768544654100267008

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