Faithful three-dimensional invariant-ring conjecture

Let $G=({\bf Z}/p)^r$ and let $V$ be a faithful three-dimensional modular representation of $G$ over a field of characteristic $p$. Its invariant ring is $\mathbf{k}[V]^G$. Faithful invariant-ring conjecture. The ring $\mathbf{k}[V]^G$ is a complete intersection with embedding dimension at most $\lceil r/2\rceil+3$. The paper describes this as the expected general bound, supported by the computed low-rank cases; the assertion for arbitrary $r$ remains open.