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<p>The algebraic <i>K</i>-theory in Quillen’s sense is developed for homological exact contexts that have been introduced by Chen and Xi (2019). In particular, we get homotopy cartesian squares of <i>K</i>-theory spectra, and infinite Mayer-Vietoris sequences of algebraic <i>K</i>-groups. These results extend the Mayer-Vietoris sequence of six terms given by Milnor (1971), and capture an excision theorem of Suslin in <i>K</i>-theory and a result of Karoubi on homotopy cartesian squares of localizations. Moreover, reduction formulas for algebraic <i>K</i>-groups are presented for the free products of finite groups, for the finite adéle rings of Dedekind domains, and for trivially twisted extensions.</p>

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Recollements of derived categories, II: K-theory of homological exact contexts

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Hongxing Chen,
  • Changchang Xi

摘要

The algebraic K-theory in Quillen’s sense is developed for homological exact contexts that have been introduced by Chen and Xi (2019). In particular, we get homotopy cartesian squares of K-theory spectra, and infinite Mayer-Vietoris sequences of algebraic K-groups. These results extend the Mayer-Vietoris sequence of six terms given by Milnor (1971), and capture an excision theorem of Suslin in K-theory and a result of Karoubi on homotopy cartesian squares of localizations. Moreover, reduction formulas for algebraic K-groups are presented for the free products of finite groups, for the finite adéle rings of Dedekind domains, and for trivially twisted extensions.