On the algebraic K-theory of Witt vectors of finite length

2011/01/10 by Vigleik Angeltveit, Angeltveit, Vigleik
Mathematics · #19D55 #55T25 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1101.1866

openalex publication_date 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a perfect field of characteristic p and let W_n(k) denote the p-typical Witt vectors of length n. For example, W_n(\mathbbF_p)=ℤ/pⁿ. We study the algebraic K-theory of W_n(k), and prove that K(W_n(k)) satisfies "Galois descent". We also compute the K-groups through a range of degrees, and show that the first p-torsion element in the stable homotopy groups of spheres is detected in K_2p-3(W_n(k)) for all n ≥ 2.

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