Power series rings and projectivity
| dc.creator | Buchweitz, R. -O. | |
| dc.creator | Flenner, H. | |
| dc.date | 2005-09-08 | |
| dc.date | 2005-11-02 | |
| dc.date.accessioned | 2026-07-07T06:42:58Z | |
| dc.date.available | 2026-07-07T06:42:58Z | |
| dc.description | We show that a formal power series ring $A[[X]]$ over a noetherian ring $A$ is not a projective module unless $A$ is artinian. However, if $(A,{\mathfrak m})$ is local, then $A[[X]]$ behaves like a projective module in the sense that $Ext^p_A(A[[X]], M)=0$ for all ${\mathfrak m}$-adically complete $A$-modules. The latter result is shown more generally for any flat $A$-module $B$ instead of $A[[X]]$. We apply the results to the (analytic) Hochschild cohomology over complete noetherian rings. | |
| dc.description | Mainly thanks to remarks and pointers by L.L.Avramov and S.Iyengar, we added further context and references. To appear in Manuscripta Mathematica. 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509180 | |
| dc.identifier | http://arxiv.org/abs/math/0509180 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102244 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13C10; 13D07; 13D03; 18G05 | |
| dc.title | Power series rings and projectivity | |
| dc.type | text |