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

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arxiv 1101.1866 v4 pith:QPT6AVUP submitted 2011-01-10 math.AT math.KT

Vigleik Angeltveit This is my paper · ORCID
classification math.ATmath.KT
keywords algebraick-theorylengthmathbbvectorswittcharacteristiccompute
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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, $W_n(\mathbb{F}_p)=\mathbb{Z}/p^n$. 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 $n \geq 2$.

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  1. On the integral algebraic K-theory of Morava K-theory

    math.AT 2026-07 conditional novelty 8.0 of 10

    For connective Morava K-theory, the paper determines algebraic K-theory group cardinalities in all degrees outside two congruence classes over finite fields, and proves even-degree groups vanish over algebraically clo...

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