MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In Stefan Schewede's paper Formal groups and stable homotopy of commutative rings, he introduces $\Gamma$-rings (ring spectra) $DB$ for any commutative ring $B$ such that the the set of 1-dimensional commutative formal group laws over $B$ is in bijection with the set of maps of ring spectra: $\mathrm{Ring}(H\mathbb{Z},DB).$ The $\Gamma$-ring $DB$ has underlying $\Gamma$-space the functor $K\mapsto \mathrm{ker}(\tilde{B}[[K]]\to\tilde{B}[[\ast]]\cong B),$ considered as a constant simplicial set.

My question is basically whether or not we can glue together such $DB$ to get some "global sections" sort of object that determines all formal group laws over all rings, and if such a thing would have some topological relationship to the Thom spectrum $MU$. Or, another perhaps similar question is, can Schwede's spectra be reinterpreted from a stacky perspective, and if so, what relationship do they bear to $\mathcal{M}_{fgl}$?


share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.