Higher limits of wider systems

Jeffrey Bergfalk; Matteo Casarosa

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arXiv · 2507.05471

Higher limits of wider systems

Jeffrey Bergfalk·Matteo Casarosa

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Abstract

Write $\mathbf{A}_\lambda$ for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal $\lambda$ to the set of natural numbers. The question of whether for any fixed $n$ the derived limit $\mathrm{lim}^n\,\mathbf{A}_\lambda$ may vanish for only a nonempty subset of the class of infinite cardinals $\lambda$ is recorded in both [Be17] and [Ban23], and bears closely on several related further ones. We answer this question in the affirmative; in fact, we show the maximal possibility, namely that this can simultaneously happen in every degree $n>1$.

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BibTeX RIS

Jeffrey Bergfalk, Matteo Casarosa. 2025-07-07. Higher limits of wider systems. https://arxiv.org/abs/2507.05471

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