论文标题
局部同质等效的质量模型结构
A Quillen model structure of local homotopy equivalences
论文作者
论文摘要
在本说明中，我们在$ \ mathbb {z}/2 \ mathbb {z} $的类别上构建了一个封闭的模型结构。当基本场是完整离散估值环$ V $的分数字段$ f $时，该模型结构的同型类别是准阿贝尔类别的派生类别$ \ overleftarrow {\ mathsf {indsf {indsf {indsf {indsf {\ mathsf {ban} _f {ban} _f）} $。此同型类别是用于完整的本地和分析循环同源性理论的适当目标。当基本字段为$ \ mathbb {c} $时，同型类别是局部和分析循环同源物的目标，用于亲生学$ \ mathbb {c} $ - 代数，其中包括pro-$ $ $ c^*$ - 代数的子类别。
In this note, we construct a closed model structure on the category of $\mathbb{Z}/2\mathbb{Z}$-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field $F$ of a complete discrete valuation ring $V$, the homotopy category of this model structure is the derived category of the quasi-abelian category $\overleftarrow{\mathsf{Ind}(\mathsf{Ban}_F)}$. This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree $V$-algebras and $\mathbb{F}$-algebras. When the base field is $\mathbb{C}$, the homotopy category is the target of local and analytic cyclic homology for pro-bornological $\mathbb{C}$-algebras, which includes the subcategory of pro-$C^*$-algebras.
