Consider something like baby Grothendieck motives, by which I'll mean classes of algebraic varieties X modulo relations [X] - [Y] = [X\Y], [X x Y] = [X] x [Y], [A] * [A^-1] = [point] where A is an affine line and `A^-1` the formal inverse. Also, the ring will be complex numbers. If you want, you can also take idempotent completion.

Now those things can be added and multiplied, so they **form a ring**, call it `M`. And for things that form a ring you can **study their `Spec`**. E.g. they have points.

**Question:** what are the scheme properties of `Spec M`? How to describe its points?

For example, one point is **Euler characteristics** `\chi \in \Spec M`, since it's additive and multiplicative. I think there's also a plane there given by Hodge numbers `h^{p,q}`, since Hodge polynomial at a given point satisfies those relations too. Are there any other points?

Any more information? 

(+ can we tag it `motives`, or better yet lower creating tag requirements to, e.g., 100?)