The small-characteristic Hilbert-series conjecture for quotient singularities

Let $V$ be a symplectic vector space over a field $\boldsymbol{F}$ of characteristic $p$, let $G$ be a finite group of order coprime to $p$ acting faithfully on $V$, and let $A$ be the algebra of regular functions on $V/G$. Let $S$ be the collection of subgroups used in formula

, and for $K\in S$ let $\overline{V^K}$ denote the relevant quotient of the fixed-point space. Let $D$ be the maximal degree of a nonzero element in $HP_0(\boldsymbol{F}[\overline{V^K}]^K)$. **Small-characteristic quotient-singularity conjecture.** Formula

holds for $h_{A/\{A,A\}}(t)$ if $p>\frac{1}{2}D+1$. The bound is proposed as part of the paper's conjectural results for small characteristic, while the source does not establish it.