If G is a finite group and k a field of characteristic p, the group algebra kG can be written uniquely as a direct product of indecomposable algebras, known as the "blocks'' of G. The representation theory of kG can now be treated one block at a time, and some blocks may be easier than others. To each block B one may associate a p-subgroup of G, called its "defect group'', which measures the difficulty of B. Very little is known in general, but blocks whose defect group is cyclic are completely understood. Working with Ricardo Franquiz Flores, we have begun to extend block theory to profinite groups. I'll explain all the words in the abstract and present a classification of the blocks of a profinite group whose defect group is (pro)cyclic -- blocks with defect group Z_p are remarkably well behaved!
Universidade Federal de Minas Gerais
Algebra, Combinatorics and Number Theory