Block theory and Brauer's first main theorem for profinite groups

We develop the local-global theory of blocks for profinite groups. Given a field k characteristic p and group G, one may express completed algebra k[[G]] as product ∏i∈IBi closed indecomposable algebras, called G. To each block B G we associate pro-p subgroup defect B, unique up to conjugacy in give several characterizations analogy with groups finite Our main theorem is version Brauer's first theorem: correspondence between D normalizer NG(D) D.