= Modular reduction of block idempotents
For a complete <discrete valuation ring> $\mathcal O$ with residue <field> $k$, class sums give bases of $Z(\mathcal OG)$ and $Z(kG)$, so reduction of the <center of an associative algebra> is surjective. <Idempotent lifting> in this complete commutative <algebra> gives a bijection of primitive <central idempotents>, hence of <blocks of a group algebra>. Corresponding <blocks of a group algebra> have the same <defect groups of a block>: <relative traces> reduce, and a lifted trace whose reduction is the block identity is a unit in its complete block center.
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