Conjecture on counting unipotent irreducible Brauer characters

Let $\mathbf{G}$ be a reductive algebraic group with Frobenius endomorphism $F$, let $G=\mathbf{G}^F$, and let $p$ be the characteristic of the defining field. For each $\ell$-special unipotent element $u$, let $\Gamma_u^\ell$ be the $\ell$-special quotient defined from the projective characters of $A_{\mathbf{G}}(u)$. Let $\alpha_\ell$ be the number of pairs $(u,x)$, where $u$ runs over $\ell$-special unipotent elements of $G$ up to $\mathbf{G}$-conjugacy and $x\in\tilde{\mathcal{M}}_\ell(\Gamma_u^\ell)$.

Counting conjecture. Suppose that $p$ is good for $\mathbf{G}$. Then $\alpha_\ell$ is the number of unipotent irreducible Brauer characters of $G$.

In characteristic zero, analogous counts use canonical quotients associated with special unipotent classes. The conjecture proposes that the $\ell$-special quotient gives the correct count in positive characteristic, including the modular setting relevant to bad primes.