On the derived invariance of cohomology theories for coalgebras

dc.creatorFarinati, Marco A.
dc.date2000-06-08
dc.date.accessioned2026-07-07T04:35:47Z
dc.date.available2026-07-07T04:35:47Z
dc.descriptionWe study the derived invariance of the cohomology theories $Hoch^*$, $H^*$ and $HC^*$ associated to coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: 1) $f:C\to D$ a quasi-isomorphism of differential graded coalgebras, 2) the existence of a "cotilting" bicomodule ${}_CT_D$. In these two cases we construct a derived-Morita equivalence context, and consequently we obtain isomorphisms $Hoch^*(C)\cong\Hoch^*(D)$ and $H^*(C)\cong H^*(D)$. Moreover, when we have a coassociative map inducing an isomorphism $H^*(C)\cong H^*(D)$ (for example when there is a quasi-isomorphism $f:C\to D$), we prove that $HC^*(C)\cong HC^*(D)$.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0006060
dc.identifierhttp://arxiv.org/abs/math/0006060
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59374
dc.subjectK-Theory and Homology
dc.subjectCommutative Algebra
dc.subject16E40; 13D07; 16E45; 16W30
dc.titleOn the derived invariance of cohomology theories for coalgebras
dc.typetext

Files

Collections