There's a theory of algebraic geometry over $\mathbb{Z}_2$-graded commutative rings, often called "[algebraic supergeometry](https://arxiv.org/abs/2008.00700)" or the theory of [superschemes](https://ncatlab.org/nlab/show/super-scheme). From what I understand, there's also a variant theory of $\mathbb{Z}$-graded algebraic geometry, for rings whose multiplication is $\mathbb{Z}$-graded commutative, satisfying $ab=(-1)^{\deg(a)\deg(b)}ba$.

Now, many structures arising in algebraic topology are not commutative, but some are instead _graded-commutative_―for instance, this is the case for the [cohomology ring](https://en.wikipedia.org/wiki/Cohomology_ring) of any space.

> **Question.** Can one use the theory of $\mathbb{Z}$-graded algebraic geometry to say something useful about some of the graded-commutative structures found in algebraic topology, such as e.g. cohomology rings?

One thing I imagine one could do is say take the ($\mathbb{Z}$-graded) $\mathrm{Spec}$ of a cohomology ring, and then study it algebro-geometrically as a scheme in the $\mathbb{Z}$-graded setting. Has this sort of strategy ever been successfully carried out?

(Of course there's DAG/SAG, which work wonderfully for the purposes of homotopy theory, but I'm nevertheless curious about this question considered from the point of view of graded-commutative algebraic geometry.)