Ind-étale versus formally étale

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-16 DOI:10.1112/blms.70025

Shubhodip Mondal, Alapan Mukhopadhyay

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Abstract

We show that when $A$ is a reduced algebra over a characteristic zero field $k$ and the module of Kähler differentials $Ω_{A / k} = 0$ , then $A$ is ind-étale, partially answering a question of Bhatt. As further applications of this result, we deduce a rigidity property of Hochschild homology and special instances of Weibel's conjecture and Vorst's conjecture without any noetherian assumptions.

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指数价差与正式价差

我们证明当A$ A$是特征零域k$ k$上的约简代数，且Kähler微分的模Ω A / k = 0$\Omega _{A/k}=0$，则A$ A$是ind- sameta，部分回答了Bhatt的问题。作为这一结果的进一步应用，我们推导出了Hochschild同调的刚性性质以及Weibel猜想和Vorst猜想的特殊实例，而不需要任何诺瑟尔假设。

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