On the derived invariance of cohomology theories for coalgebras
| dc.creator | Farinati, Marco A. | |
| dc.date | 2000-06-08 | |
| dc.date.accessioned | 2026-07-07T04:35:47Z | |
| dc.date.available | 2026-07-07T04:35:47Z | |
| dc.description | We 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.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0006060 | |
| dc.identifier | http://arxiv.org/abs/math/0006060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59374 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Commutative Algebra | |
| dc.subject | 16E40; 13D07; 16E45; 16W30 | |
| dc.title | On the derived invariance of cohomology theories for coalgebras | |
| dc.type | text |