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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2003
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| 001 | PAPER-4890 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203429.0 | ||
| 008 | 190411s2003 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0043283829 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Farinati, M.A. | |
| 245 | 1 | 3 | |a On the Derived Invariance of Cohomology Theories for Coalgebras |
| 260 | |c 2003 | ||
| 270 | 1 | 0 | |m Farinati, M.A.; Dto. de Matemática FCEyN, Uniyersidad de Buenos Aires, Cdad. Universitaria Pab I. (1428), Buenos Aires, Argentina; email: mfarinat@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Doi, Y., Homological coalgebra (1981) J. Math. Soc. Japan., 33 (1), pp. 31-50 | ||
| 504 | |a Hartshorne, R., Residues and Duality (1966) Lecture Notes in Math., 20. , Springer, New York | ||
| 504 | |a Farinati, M.A., (1999) Teorías de Cohomología de Coálgebras, , PhD thesis, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires | ||
| 504 | |a Farinati, M.A., Solotar, A.L., Morita-Takeuchi equivalence, cohomology of coalgebras and Azumaya coalgebras (1998) Lecture Notes in Pure and Appl. Math., 197. , Rings, Hopf Algebras, and Brauer Groups, Marcel Dekker, New York | ||
| 504 | |a Farinati, M.A., Solotar, A.L., Cyclic homology of coalgebras Lecture Notes in Pure and Appl. Math., , Hopf Algebras and Quantum Groups, Marcel Dekker, New York | ||
| 504 | |a Keller, B., Tilting theory and differential graded algebras (1994) Proc. Nato ARW on Representation of Algebras and Related Topics, , V. Dlab and L. Scott (eds), Kluwer Acad. Publ., Dordrecht | ||
| 504 | |a Gelfand, S.I., Manin, Y.I., (1996) Methods of Homological Algebra, , Springer, New York | ||
| 504 | |a Takeuchi, M., Monta theorems for categories of comodules (1977) J. Fac. Sci. Univ. Tokyo, 24, pp. 1483-1528 | ||
| 520 | 3 | |a 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). |l eng | |
| 593 | |a Dto. de Matemática FCEyN, Uniyersidad de Buenos Aires, Cdad. Universitaria Pab I. (1428), Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a COALGEBRAS |
| 690 | 1 | 0 | |a DERIVED CATEGORIES |
| 690 | 1 | 0 | |a HOCHSCHILD HOMOLOGY |
| 690 | 1 | 0 | |a GEOMETRY |
| 690 | 1 | 0 | |a PROBLEM SOLVING |
| 690 | 1 | 0 | |a THEOREM PROVING |
| 690 | 1 | 0 | |a DERIVED CATEGORIES |
| 650 | 1 | 7 | |2 spines |a ALGEBRA |
| 773 | 0 | |d 2003 |g v. 6 |h pp. 303-331 |k n. 3 |p Algebr Represent Theory |x 1386923X |t Algebras and Representation Theory | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-0043283829&doi=10.1023%2fA%3a1025114311299&partnerID=40&md5=e82bfb42284d0ebf04d6b4842442e3fa |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1023/A:1025114311299 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_1386923X_v6_n3_p303_Farinati |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v6_n3_p303_Farinati |y Registro en la Biblioteca Digital |
| 961 | |a paper_1386923X_v6_n3_p303_Farinati |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 65843 | ||