Derived Category of Squarefree Modules and Local Cohomology with Monomial Ideal Support
| dc.creator | Yanagawa, Kohji | |
| dc.date | 2003-03-10 | |
| dc.date.accessioned | 2026-07-07T04:55:53Z | |
| dc.date.available | 2026-07-07T04:55:53Z | |
| dc.description | A "squarefree module" over a polynomial ring $S = k[x_1, .., x_n]$ is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals systematically. Let $Sq$ be the category of squarefree modules. Then the derived category $D^b(Sq)$ of $Sq$ has three duality functors which act on $D^b(Sq)$ just like three transpositions of the symmetric group $S_3$ (up to translation). This phenomenon is closely related to the Koszul dulaity (in particular, the Bernstein-Gel'fand-Gel'fand correspondence). We also study the local cohomology module $H_{I_Δ}^i(S)$ at a Stanley-Reisner ideal $I_Δ$ using squarefree modules. Among other things, we see that Hochster's formula on the Hilbert function of $H_m^i(S/I_Δ)$ is also a formula on the characteristic cycle of $H_{I_Δ}^{n-i}(S)$ as a module over the Weyl algebra $S<\partial_1, ..., \partial_n >$ (if $chara(k)=0$). | |
| dc.description | 21pages, to appear in J. Math. Soc. Japan. I distributed the earlier version of this paper in 2000, but the paper has been totally revised | |
| dc.identifier | https://arxiv.org/abs/math/0303110 | |
| dc.identifier | http://arxiv.org/abs/math/0303110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66739 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13D02, 13D45, 13F55, 18E30 | |
| dc.title | Derived Category of Squarefree Modules and Local Cohomology with Monomial Ideal Support | |
| dc.type | text |