The blockwise Alperin weight conjecture asserts that the number 
of irreducible Brauer characters
in a block 
equals the number of conjugacy classes of weights
assigned to 
. A 
-weight is a pair 
consisting of a 
-subgroup 
and a defect-zero ordinary irreducible group
character of 
.
Here defect zero means that the largest power of 
dividing 
equals that dividing the group
order. Weights are assigned to blocks by Brauer block induction, and conjugacy
acts simultaneously on both parts.
This is a numerical equality rather than a specified equivariant bijection.
