同调光滑连通上链DG代数的一个注记

毛雪峰, 谢建峰

数学学报 ›› 2018, Vol. 61 ›› Issue (5) : 715-728.

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PDF(574 KB)
数学学报 ›› 2018, Vol. 61 ›› Issue (5) : 715-728. DOI: 10.12386/A2018sxxb0066
论文

同调光滑连通上链DG代数的一个注记

    毛雪峰1,2, 谢建峰1
作者信息 +

A Note on Homologically Smooth Connected Cochain DG Algebras

    Xue Feng MAO1,2, Jian Feng XIE1
Author information +
文章历史 +

摘要

本文给出了有关同调光滑连通上链微分分次(简称DG)代数的两个重要结论.具体地说,当A是同调光滑连通上链DG代数且其同调分次代数HA)是诺特分次代数时,证明DfgA)中的任意Koszul DG A-模都是紧致的.另外,当A是Kozul连通上链DG代数且其同调分次代数HA)是有平衡对偶复形的诺特分次代数时,证明A的同调光滑性质等价于DfgA)=DcA).

Abstract

In this paper, we obtain two interesting results on homologically smooth connected cochain DG algebras. More precisely, we show that any Koszul DG A-module in Dfg(A) is compact, when A is a homologically smooth connected cochain DG algebra with a Noetherian cohomology graded algebra H(A). We prove that the homologically smoothness of A is equivalent to Dfg(A)=Dc(A), if A is a Koszul connected cochain DG algebra such that H(A) is a Noetherian graded algebra with a balanced dualizing complex.

关键词

同调光滑DG代数 / Koszul DG代数 / 紧致DG模 / DG自由class

Key words

homologically smooth DG algebra / Koszul DG algebra / DG free class / compact DG module

引用本文

导出引用
毛雪峰, 谢建峰. 同调光滑连通上链DG代数的一个注记. 数学学报, 2018, 61(5): 715-728 https://doi.org/10.12386/A2018sxxb0066
Xue Feng MAO, Jian Feng XIE. A Note on Homologically Smooth Connected Cochain DG Algebras. Acta Mathematica Sinica, Chinese Series, 2018, 61(5): 715-728 https://doi.org/10.12386/A2018sxxb0066

参考文献

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基金

国家自然科学基金资助项目(11001056)

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