论文标题
完整模块的同质理论
The homotopy theory of complete modules
论文作者
论文摘要
给定一个交换戒指$ r $和有限生成的理想$ i $，可以考虑$ i $ ai $ - $ l_0^i $ complete的类别和派生的$ i $ complete complectes。在对理想$ i $的温和假设下，这三个完成概念的概念相互作用良好。我们考虑$ i $ - $ afiper完成的类别，$ l_0^i $ complete和派生的$ i $ - complete complectes，并证明它们呈现相同的同质理论。鉴于戒指同构$ r \ to s $，然后我们为完整的$ r $ complexes类别提供了必要和足够的条件，以及完整的$ s $ complexes类别以具有同等的同型理论。这恢复并概括了Sather-Wagstaff和Wicklein在扩展的本地（CO）同源性上的结果。
Given a commutative ring $R$ and finitely generated ideal $I$, one can consider the classes of $I$-adically complete, $L_0^I$-complete and derived $I$-complete complexes. Under a mild assumption on the ideal $I$ called weak pro-regularity, these three notions of completions interact well. We consider the classes of $I$-adically complete, $L_0^I$-complete and derived $I$-complete complexes and prove that they present the same homotopy theory. Given a ring homomorphism $R \to S$, we then give necessary and sufficient conditions for the categories of complete $R$-complexes and the categories of complete $S$-complexes to have equivalent homotopy theories. This recovers and generalizes a result of Sather-Wagstaff and Wicklein on extended local (co)homology.
