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arxiv: 1101.1866 · v4 · pith:QPT6AVUPnew · submitted 2011-01-10 · 🧮 math.AT · math.KT

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

classification 🧮 math.AT math.KT
keywords algebraick-theorylengthmathbbvectorswittcharacteristiccompute
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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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