Relative K-theory via 0-cycles in finite characteristic

Gupta, Rahul; Krishna, Amalendu

doi:10.2140/akt.2021.6.673

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Relative K-theory via 0-cycles in finite characteristic

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Krishna, Amalendu
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2140/akt.2021.6.673
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https://doi.org/10.48550/arXiv.1910.06630
(Preprint)

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Citation

Gupta, R., & Krishna, A. (2021). Relative K-theory via 0-cycles in finite characteristic. Annals of K-Theory, 6(4), 673-712. doi:10.2140/akt.2021.6.673.

Cite as: https://hdl.handle.net/21.11116/0000-000A-A008-8

Abstract

Let $R$ be a regular semi-local ring, essentially of finite type over an
infinite perfect field of characteristic $p \ge 3$. We show that the cycle
class map with modulus from an earlier work of the authors induces a
pro-isomorphism between the additive higher Chow groups of relative 0-cycles
and the relative $K$-theory of truncated polynomial rings over $R$. This
settles the problem of equating 0-cycles with modulus and relative $K$-theory
of such rings via the cycle class map.