Dualizing complex of the incidence algebra of a finite regular cell complex
| dc.creator | Yanagawa, Kohji | |
| dc.date | 2004-07-22 | |
| dc.date | 2005-05-02 | |
| dc.date.accessioned | 2026-07-07T05:10:35Z | |
| dc.date.available | 2026-07-07T05:10:35Z | |
| dc.description | Let $Σ$ be a finite regular cell complex with $\emptyset \in Σ$, and regard it as a partially ordered set (poset) by inclusion. Let $R$ be the incidence algebra of the poset $Σ$ over a field $k$. Corresponding to the Verdier duality for constructible sheaves on $Σ$, we have a dualizing complex $w \in D^b(mod_{R \otimes_k R})$ giving a duality functor from $D^b(mod_R)$ to itself. $w$ satisfies the Auslander condition. Our duality is somewhat analogous to the Serre duality for projective schemes ($\emptyset$ plays a similar role to that of "irrelevant ideals"). If $H^i(w) \ne 0$ for exactly one $i$, then the underlying topological space of $Σ$ is Cohen-Macaulay (in the sense of the Stanley-Reisner ring theory). The converse also holds when $Σ$ is a simplicial complex. $R$ is always a Koszul ring with $R^! \cong R^op$. The relation between the Koszul duality for $R$ and the Verdier duality is discussed. This result is a variant of a theorem of Vybornov. The Mobius function of the poset $\hatΣ$ is also discussed. | |
| dc.description | 18 pages. The results are almost same. But the exposition has been totally revised emphasizing combinatorial aspects | |
| dc.identifier | https://arxiv.org/abs/math/0407383 | |
| dc.identifier | http://arxiv.org/abs/math/0407383 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71971 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 16E05; 32S60; 13F55; 06A10 | |
| dc.title | Dualizing complex of the incidence algebra of a finite regular cell complex | |
| dc.type | text |