对数TAQ与对数THH的关系

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2020-04-07 DOI:10.4171/dm/839

T. Lundemo

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引用次数: 4

摘要

从增广环谱不可分解的角度给出了对数拓扑Andre-Quillen同调的一种新描述。新的描述允许我们将对数TAQ解释为抽象的余切复，并导致对数拓扑Hochschild同调的一个线性下降公式。后者类似于Weibel-Geller关于离散环Hochschild同调的结果，以及McCarthy-Minasian和Mathew关于拓扑Hochschild同调的结果。我们还总结和澄清了用普通THH和TAQ定义的形式完备性概念的类似结果。

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On the relationship between logarithmic TAQ and logarithmic THH

We provide a new description of logarithmic topological Andre-Quillen homology in terms of the indecomposables of an augmented ring spectrum. The new description allows us to interpret logarithmic TAQ as an abstract cotangent complex, and leads to an etale descent formula for logarithmic topological Hochschild homology. The latter is analogous to results of Weibel-Geller for Hochschild homology of discrete rings, and of McCarthy-Minasian and Mathew for topological Hochschild homology. We also summarize and clarify analogous results relating notions of formal etaleness defined in terms of ordinary THH and TAQ.

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来源期刊

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.