Abstract
A cohomological support, $\operatorname{Supp}^*_{\mathcal A}(M)$, is defined for finitely generated modules $M$ over a left noetherian ring $R$, with respect to a ring $\mathcal A$ of central cohomology operations on the derived category of $R$-modules. It is proved that if the $\mathcal A$-module $\operatorname{Ext}^*_R(M,M)$ is noetherian and $\operatorname{Ext}^*_R(M,R)=0$ for $i\gg0$, then every closed subset of $\operatorname{Supp}^*_{\mathcal A}(M)$ is the support of some finitely generated $R$-module. This theorem specializes to known realizability results for varieties of modules over group algebras, over local complete intersections, and over finite dimensional algebras over a field. The theorem is also used to produce large families of finitely generated modules of finite projective dimension over commutative local noetherian rings.
Citation
Luchezar L. Avramov. Srikanth B. Iyengar. "Constructing modules with prescribed cohomological support." Illinois J. Math. 51 (1) 1 - 20, Spring 2007. https://doi.org/10.1215/ijm/1258735320
Information