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.
