论文标题
通过DG环的有限维度猜想
The finitistic dimension conjecture via DG-rings
论文作者
论文摘要
给定一个关联戒指$ a $，我们提出了一种新的方法，用于建立大型有限型投影维度$ \ operatatorName {fpd}（a）$的有限。这个想法是要找到一个足够好的非物性分级分级环$ b $，以便$ \ mathrm {h}^0（b）= a $，因此$ \ operatorAtorName {fpd}（b）<\ infty $。我们表明，只要$ a $是noetherian，并且具有非交易性双重化综合体，我们总是可以找到这样的$ b $。然后，我们使用$ \ operatatorName {\ mathsf {d}}（b）$和$ \ operatatorName {\ Mathsf {d}}（\ Mathrm {h}^0（b））$之间的紧密关系。作为一个应用程序，我们概括了Rickard的最新状态，以$ \ operatoTorname {fpd}（a）<\ infty $在$ \ peripatatorName {\ m athsf {\ mathsf {d}}}（a）$方面，从有限的尺寸代数中，从一个有限的尺寸代数到所有noetherian noetherian noetherian noetherian rings complects confecter a diality complects a dialiate a dialiate a ializations a。
Given an associative ring $A$, we present a new approach for establishing the finiteness of the big finitistic projective dimension $\operatorname{FPD}(A)$. The idea is to find a sufficiently nice non-positively graded differential graded ring $B$ such that $\mathrm{H}^0(B) = A$ and such that $\operatorname{FPD}(B) < \infty$. We show that one can always find such a $B$ provided that $A$ is noetherian and has a noncommutative dualizing complex. We then use the intimate relation between $\operatorname{\mathsf{D}}(B)$ and $\operatorname{\mathsf{D}}(\mathrm{H}^0(B))$ to deduce results about $\operatorname{FPD}(A)$. As an application, we generalize a recent sufficient condition of Rickard, for $\operatorname{FPD}(A) < \infty$ in terms of generation of $\operatorname{\mathsf{D}}(A)$ from finite dimensional algebras over a field to all noetherian rings which admit a dualizing complex.
