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Equivariant algebraic K-functors for \(\Gamma \)-rings

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Abstract

This is an attempt to extend to algebraic K-theory our approach to group actions in homological algebra that could be called an introduction to \(\Gamma \)-algebraic K-theory. For \(\Gamma \)-rings, the Milnor algebraic K-theory and Swan algebraic K-functors are introduced and investigated. In particular, the Matsumoto conjecture related to the symbol group, and the Milnor conjectures related to Witt algebras and Chow groups for \(\Gamma \)-rings are extended.

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Acknowledgements

The author thanks the referee for careful reading of the manuscript and for giving constructive remarks that substantially improved the quality of presentation of the paper.

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  1. A. Razmadze Mathematical Institute of Tbilisi State University, 6, Tamarashvili Str., 0179, Tbilisi, Georgia

    Hvedri Inassaridze

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  1. Hvedri Inassaridze
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Correspondence to Hvedri Inassaridze.

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Dedicated to my mother, Nino Inassaridze.

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Inassaridze, H. Equivariant algebraic K-functors for \(\Gamma \)-rings. European Journal of Mathematics 9, 115 (2023). https://doi.org/10.1007/s40879-023-00712-2

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  • DOI: https://doi.org/10.1007/s40879-023-00712-2

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