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arXiv · 1905.03102

Rigidity in equivariant algebraic $K$-theory

Niko Naumann·Charanya Ravi
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Abstract

If $(R,I)$ is a henselian pair with an action of a finite group $G$ and $n\ge 1$ is an integer coprime to $|G|$ and such that $n\cdot |G|\in R^*$, then the reduction map of mod-$n$ equivariant $K$-theory spectra \[ K^G(R)/n\stackrel{\simeq}{\longrightarrow} K^G(R/I)/n\] is an equivalence. We prove this by revisiting the recent proof of non-equivariant rigidity by Clausen, Mathew, and Morrow.

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Niko Naumann, Charanya Ravi. 2019-05-08. Rigidity in equivariant algebraic $K$-theory. https://doi.org/10.2140/akt.2020.5.141

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