All Questions

One may argue that $\mathbb{S}$ is more correct than $\mathbb{Z}$. Can anyone make it more explicitly? For example, what information will be lost if we work in $\mathbb{Z}$ instead of $\mathbb{S}$？ ...

It is known that the only "fields" in stable homotopy theory, after localizing at a prime $p$, are Eilenberg-Mac Lane spectra for fields and the Morava K-theories (this is true in a few senses: these ...

We fix $p$ prime and $n$ a natural number. We let $K(n)$ be the $2(p^{n}-1)$-periodic Morava $K$-theory, i.e. $K(n)_*=\mathbb{F}_p[v_n^{\pm 1}]$ with $|v_n|=2(p^n-1)$. I distinctly recall that we ...