Green correspondence for virtually pro-p groups

Brauer theory for profinite groups

“…]-mod is the object of study in the modular representation theory of profinite groups, considered in [9] and [8]. Both categories have enough projectives.…”

Blocks of profinite groups with cyclic defect group

“…The study of the modular representation theory of profinite groups was begun in [12, 13], while the study of blocks and defect groups has been initiated recently in [5]. In this article we classify, in Theorem 4.3, the blocks of an arbitrary profinite group whose defect groups are cyclic (meaning either a finite cyclic $$p$$‐group or the $$p$$‐adic integers $$\mathbb {Z}_p$$): they are Brauer tree algebras in strict analogy with the finite case.…”

“…Blocks with cyclic defect group have an explicit description as so-called 'Brauer tree algebras'. For a clear and encyclopedic discussion of the block theory of finite groups we recommend [10,11].The study of the modular representation theory of profinite groups was begun in [12,13], while the study of blocks and defect groups has been initiated recently in [5]. In this article we classify, in Theorem 4.3, the blocks of an arbitrary profinite group whose defect groups are cyclic (meaning either a finite cyclic 𝑝-group or the 𝑝-adic integers ℤ 𝑝 ): they are Brauer tree algebras in strict analogy with the finite case.…”

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

“…This suggests that the block theoretic approach to the representation theory of profinite groups will be as central to the theory as it is with finite groups. For comparison, we note that with modules, conditions on the group are frequently required to prove the most powerful results -see for instance [14,15].…”