Remarks on iterations of the 𝔸1-chain connected components construction

IF 0.5 Q3 MATHEMATICS
Chetan T. Balwe, B. Rani, Anand Sawant
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引用次数: 1

Abstract

We show that the sheaf of $\mathbb A^1$-connected components of a Nisnevich sheaf of sets and its universal $\mathbb A^1$-invariant quotient (obtained by iterating the $\mathbb A^1$-chain connected components construction and taking the direct limit) agree on field-valued points. This establishes an explicit formula for the field-valued points of the sheaf of $\mathbb A^1$-connected components of any space. Given any natural number $n$, we construct an $\mathbb A^1$-connected space on which the iterations of the naive $\mathbb A^1$-connected components construction do not stabilize before the $n$th stage.
关于𝔸1-chain连接组件构造迭代的备注
我们证明了Nisnevich集合的$\mathbb A^1$连通分量及其通称$\mathbb A^1$不变商(通过迭代$\mathbb A^1$链连通分量构造并取直接极限得到)在域值点上一致。这为任意空间的$\mathbb A^1$连通分量集的场值点建立了一个显式公式。给定任意自然数$n$,我们构造一个$\mathbb A^1$连通空间,在该空间上,$\mathbb A^1$连通分量构造的迭代在$n$阶之前不稳定。
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来源期刊
Annals of K-Theory
Annals of K-Theory MATHEMATICS-
CiteScore
1.10
自引率
0.00%
发文量
12
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