Homotopy Invariance of K-groups using Grayson's Technique

2025/08/07 by Banerjee, Sourayan
#18E10 Secondary #19D06 (Primary) 19D35 #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2508.05184

Abstract

Homotopy invariance of K-theory has always been a point of interest. In this article, with the help of the generators of NilK-groups using Grayson's technique, it is shown that if R is a Prüfer domain, then K_n(R) ≅ K_n(R[s]) for all n>0. This is a specific case of the already published work of the author and Vivek Sadhu. However, contrary to the method used before, we specifically prove the isomorphism by showing that NilK-groups vanish.

Citations

• On the generators of Nil K-groups
• Algebraic proofs of some fundamental theorems in algebraic K-theory

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• Homotopy invariance of higher K-theory for abelian categories
• Kervaire Invariant One [after M. A. Hill, M. J. Hopkins, and D. C. Ravenel]
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