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...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_1386923X_v6_n3_p303_Farinati |
| Aporte de: |
| id |
todo:paper_1386923X_v6_n3_p303_Farinati |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_1386923X_v6_n3_p303_Farinati2023-10-03T16:12:23Z On the Derived Invariance of Cohomology Theories for Coalgebras Farinati, M.A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, M.A. 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). |
| format |
JOUR |
| author |
Farinati, M.A. |
| author_facet |
Farinati, M.A. |
| author_sort |
Farinati, M.A. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_1386923X_v6_n3_p303_Farinati |
| work_keys_str_mv |
AT farinatima onthederivedinvarianceofcohomologytheoriesforcoalgebras |
| _version_ |
1782029136732094464 |