4 problems

Hazrat's conjecture. The following are equivalent:

Equivariant K-theory classification conjecture. There is an order-preserving $\mathbb{Z}[x,x^{-1}]$-module isomorphism

Generating-moves conjecture. In all six cases, the equivalence relation is generated by the moves that leave the graphs invariant in the relevant sense. Explicitly,

Let $E$ be a graph and let $C^*(E)$ be its graph $C^*$-algebra. Suppose that $C^*(E)$ has finitely many ideals, and write…