A reduction theorem for the Alperin weight conjecture

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The inductive Alperin–McKay and Blockwise Alperin Weight conditions for blocks with cyclic defect groups and odd primes (2013, unknown): “1 of [34] establishes there an equivariant bijection for the non-blockwise version of the inductive Alperin Weight condition for quasisimple groups with cyclic Sylow p-subgroups, and thereby proves this inductive condition in the case where the outer automorphism group of the quasisimple group is cy”
On the inductive Alperin–McKay and Alperin weight conjecture for groups with abelian Sylow subgroups (2014, background): “In the recent past, both conjectures have been reduced to certain (stronger) statements about finite simple groups [18, 25].”