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Full computation of the algebraic K-groups K_n(Z) of the integers

Determine the algebraic K-theory groups K_n(Z) for all degrees n, completing the full computation of the algebraic K-theory of the ring of integers.

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Background

In analyzing K(\underline{Z}), the authors observe that K(Z) appears as a retract, which limits the extent of computability for K(\underline{Z}) given the state of knowledge about K(Z).

They explicitly note that the complete determination of K_n(Z) is a longstanding and difficult open problem, which blocks a full computation of the K-groups for \underline{Z}.

References

Since the full computation of $K_n(Z)$ is an extremely difficult open problem, we should not expect to be able to compute all $K$-groups of $\underline{Z}$.

The algebraic $K$-theory of Green functors (2508.14207 - Chan et al., 19 Aug 2025) in Section 6.2 (The K-theory of \underline{Z}), Remark