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Nov 24, 2020 at 22:12 history edited John Rognes CC BY-SA 4.0
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Nov 24, 2020 at 21:24 comment added Dylan Wilson Sorry for the bump on this old answer, but just to point out that this does indeed come from a K\"unneth thingy: we have $\mathbb{Z} \wedge \mathbb{Z}= (\mathbb{Z}\wedge \mathrm{BP})\otimes_{\mathrm{BP}} \mathbb{Z}$. Then $\mathbb{Z}$ is the tensor product in BP-modules of all the BP/v_i, and the image of v_i in homology is p times $\overline{\xi}_i$ (at odd primes) and 2 times $\overline{\zeta}_i^2$ at 2, whence the decomposition above. (everything p-local above)
Jun 5, 2013 at 15:18 comment added Sean Tilson This is a great answer. It is a fair bit suggestive of some sort of decomposition of $H\mathbb{Z}_{(2)*}H\mathbb{Z}_{(2)}$. What I mean is that the right hand side looks like it would really like to be a K\"{u}nneth spectral seqeunce.
Jun 5, 2013 at 11:34 history answered John Rognes CC BY-SA 3.0