On the derived invariance of cohomology theories for coalgebras

FARINATI, MARCO ANDRÉS

Algebras and Representation Theory

SPRINGER

Año: 2003 vol. 6 p. 303 - 331

1386-923X

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: CD 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: CD), we prove that HC*(C)HC*(D).