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arXiv 2405.020652024-05math.KT

不稳定代数K-理论：同调稳定性及其他观察

Unstable algebraic K-theory: homological stability and other observations

Mikala Ørsnes Jansen

备注：: 95 pages. Comments welcome! v2: better homological stability results and improved exposition

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AI总结：

本文研究约化Borel-Serre范畴的稳定性性质，证明其同调稳定性优于一般线性群，并为其作为Yuan部分代数K-理论的显式模型提供了依据。

摘要：

我们研究了约化Borel-Serre范畴的稳定性性质；这些范畴在先前工作中被引入，作为不稳定代数K-理论的一个模型。我们发现它们表现出比一般线性群更好的同调稳定性性质。我们还证明它们为Yuan的部分代数K-理论提供了一个显式模型。

英文摘要：

We investigate stability properties of the reductive Borel-Serre categories; these were introduced as a model for unstable algebraic K-theory in previous work. We see that they exhibit better homological stability properties than the general linear groups. We also show that they provide an explicit model for Yuan's partial algebraic K-theory.

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