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arXiv · 2603.13692

A general Mayer-Vietoris sequence in algebraic $K$-theory

Yakun Zhang
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Abstract

This paper investigates the Mayer-Vietoris sequence for the Milnor square. While such sequences often involve elusive intermediate terms, we provide an explicit characterization of the key group $X$ in a new, more general variant of the sequence. By identifying $X$ as a categorical pullback, we provide a full, constructive proof of the modified Mayer-Vietoris sequence. Furthermore, we show that $X$ fits into a structural exact sequence involving the relative $K$-groups $K_{*}(A, B, I)$. Finally, we provide a homotopy-theoretic description of $X$ as the homotopy group of a suitable fiber, clarifying its structure, kernel , and image.

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Yakun Zhang. 2026-03-14. A general Mayer-Vietoris sequence in algebraic $K$-theory. https://arxiv.org/abs/2603.13692

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