On the inductive Alperin–McKay and Alperin weight conjecture for groups with abelian Sylow subgroups

We study the inductive Alperin–McKay conjecture, the inductive Isaacs–Navarro refinement and the inductive blockwise Alperin weight conjecture for groups of Lie type in the generic case of abelian Sylow ℓ-subgroups. We also show that the alternating groups, the Suzuki groups and the Ree groups satisfy the inductive condition necessary for Späthʼs reduction of the blockwise Alperin weight conjecture to the case of simple groups.