kt.k theory homology - Any reason why K_23(Z) has order 65520?

More generally, if $F$ is a number field with ring of integers $mathfrak{o}$, and $zeta_F^ast(m)$ is the first nonzero coefficient in the Taylor expansion of $zeta_F$ at $m$, then Lichtenbaum (and Quillen) conjectured that $|zeta_F^ast(1-i)|=frac{# K_{2i-2}(mathfrak{o})_{text{tors}}}{# K_{2i-1}(mathfrak{o})_{text{tors}}}$, times a regulator and some power of 2 (which I believe is not understood in general, although some progress was made on this in Ion Rada's PhD thesis). Hence, odd $K$ groups are related to the denominators of the Bernoulli numbers, and the even ones are related to the numerators. Also, not much cancellation occurs; I think the two $K$-groups can only share factors of 2.

The Voevodsky-Rost theorem might prove the Lichtenbaum conjecture, but I haven't seen anyone come out and say definitely that this is the case.

I don't have much intuition for this, except that the $K$-groups seem to be objects that like to map into étale cohomology groups. In this paper (link to MathSciNet), Soulé constructs Chern class maps from certain $K$-groups to étale cohomology groups. Furthermore, these maps frequently have small (or trivial) kernels and cokernels. I suppose the idea, then, is that $K$-theory is supposed to be a slightly better behaved version of étale cohomology, at least for the purpose of understanding zeta functions.

The rank of $K$-groups of rings of integers was computed by Quillen in the early 70's: it's rank 1 in dimension 0, rank $r_1+r_2-1$ in dimension 1 (Dirichlet's unit theorem), rank 0 in even dimensions $>0$, rank $r_1+r_2$ in dimensions $1pmod 4$ except 1, and rank $r_2$ in dimensions $3pmod 4$.

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