论文标题
交换DG环的有限维度
Finitistic dimensions over commutative DG-rings
论文作者
论文摘要
在本文中，我们研究了具有有限幅度的合理性noetherian非阳性DG环的有限维度。我们证明，这种DG-RING上的任何DG-MODULE $ M $ M $都满足$ \ Mathrm {projdim} _a（m）\ Leq \ Mathrm {dim}（\ Mathrm {h}^0（a）） - \ inf（m）$。我们进一步提供具有规定的投影尺寸的DG模型的明确结构，并推断出大的有限型投影维度满足$ \ Mathrm {dimrm {dimrm {\ mathrm {h}^0（a）） - \ m armp}（amp}（amp}（a amp}（A） \ mathrm {dim}（\ mathrm {h}^0（a））$。此外，我们证明存在达到绑定的DG环。作为一种直接应用，我们证明了派生的同源性代数的衍生hochschild（CO）同源性的新结果。
In this paper we study the finitistic dimensions of commutative noetherian non-positive DG-rings with finite amplitude. We prove that any DG-module $M$ of finite flat dimension over such a DG-ring satisfies $\mathrm{projdim}_A(M) \leq \mathrm{dim}(\mathrm{H}^0 (A)) - \inf(M)$. We further provide explicit constructions of DG-modules with prescribed projective dimension and deduce that the big finitistic projective dimension satisfies the bounds $\mathrm{dim}(\mathrm{H}^0 (A)) - \mathrm{amp}(A) \leq \mathsf{FPD}(A) \leq \mathrm{dim}(\mathrm{H}^0(A))$. Moreover, we prove that DG-rings exist which achieve either bound. As a direct application, we prove new vanishing results for the derived Hochschild (co)homology of homologically smooth algebras.
