Alperin–McKay–Navarro conjecture

Let $G$ be a finite group, let $p$ be a prime, and let $B$ be a $p$-block of $G$ with defect group $D$. Let $b$ be the Brauer correspondent of $B$ in $N_G(D)$. Let $\mathcal H$ be the subgroup of $\operatorname{Gal}(\mathbb{Q}_{|G|}/\mathbb{Q})$ generated by the field automorphisms sending each $p'$-root of unity $\xi$ to $\xi^{p^e}$ for some integer $e$, and let $\mathcal H_B$ be the stabilizer of $B$ under this action. Write $\operatorname{Irr}_0(B)$ for the height-zero irreducible characters in $B$. Alperin–McKay–Navarro conjecture. There is an $\mathcal H_B$-equivariant bijection

$$\operatorname{Irr}_0(B)\longrightarrow\operatorname{Irr}_0(b).$$

This is the equivariant refinement of the Alperin–McKay conjecture, comparing height-zero characters of a block with those of its Brauer correspondent. Its status is not resolved in the supplied text.